Finite Group Databasebeta

← Group #72236272

Character table — Group #72236272

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112
size1111222222444444444444444488888816161616161616161616161616161616161616161616161611112222224444444444444444888888161616161616161616161616161616161616161616161616
order1222222222222222222222444422224424444444444444448888888822222222222222222222224444222244244444444444444488888888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11-1-1111-1-1iiii−i−i−i−iiiii−i−i−i−i111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11-1-1111-1-1iiii−i−i−i−iiiii−i−i−i−i
χ6111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11-1-1111-1-1−i−i−i−iiiii−i−i−i−iiiii111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11-1-1111-1-1−i−i−i−iiiii−i−i−i−iiiii
χ7111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1-111iiii−i−i−i−i−i−i−i−iiiii111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1-111iiii−i−i−i−i−i−i−i−iiiii
χ8111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1-111−i−i−i−iiiiiiiii−i−i−i−i111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1-111−i−i−i−iiiiiiiii−i−i−i−i
χ911111111111111-1-1-1-111111111-1-1-1-1-1-11-1-11-1-11111-1-111-1-111-1-111-1-111111111111111-1-1-1-111111111-1-1-1-1-1-11-1-11-1-11111-1-111-1-111-1-111-1-1
χ1011111111111111-1-1-1-111111111-1-1-1-1-1-11-1-11-1-111-1-111-1-111-1-111-1-11111111111111111-1-1-1-111111111-1-1-1-1-1-11-1-11-1-111-1-111-1-111-1-111-1-111
χ1111111111111111-1-1-1-111111111-1-1-1-1-1-1-111-111-1-111-1-111-1-1-1-111-1-11111111111111111-1-1-1-111111111-1-1-1-1-1-1-111-111-1-111-1-111-1-1-1-111-1-111
χ1211111111111111-1-1-1-111111111-1-1-1-1-1-1-111-111-1-1-1-111-1-11111-1-111-1-111111111111111-1-1-1-111111111-1-1-1-1-1-1-111-111-1-1-1-111-1-11111-1-111-1-1
χ1311111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1ii−i−i−i−iiiii−i−i−i−iii11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1ii−i−i−i−iiiii−i−i−i−iii
χ1411111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1−i−iiiii−i−i−i−iiiii−i−i11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1−i−iiiii−i−i−i−iiiii−i−i
χ1511111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111ii−i−i−i−iii−i−iiiii−i−i11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111ii−i−i−i−iii−i−iiiii−i−i
χ1611111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111−i−iiiii−i−iii−i−i−i−iii11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111−i−iiiii−i−iii−i−i−i−iii
χ172222222222-2-2-2-222222222-2-2-2-2-2-222-2-20000000000000000000000002222222222-2-2-2-222222222-2-2-2-2-2-222-2-2000000000000000000000000
χ182222222222-2-2-2-22222-2-2-2-22222-2-2-2-2220000000000000000000000002222222222-2-2-2-22222-2-2-2-22222-2-2-2-222000000000000000000000000
χ192222222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-2220000000000000000000000002222222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-222000000000000000000000000
χ202222222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-20000000000000000000000002222222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2000000000000000000000000
χ212222-2-2-2-22222-2-200002-22-22-22-200000002-202-20000000000000000002222-2-2-2-22222-2-200002-22-22-22-200000002-202-2000000000000000000
χ222222-2-2-2-22222-2-200002-22-22-22-20000000-220-220000000000000000002222-2-2-2-22222-2-200002-22-22-22-20000000-220-22000000000000000000
χ232222-2-2-2-22222-2-20000-22-22-22-2200000002-20-220000000000000000002222-2-2-2-22222-2-20000-22-22-22-2200000002-20-22000000000000000000
χ242222-2-2-2-22222-2-20000-22-22-22-220000000-2202-20000000000000000002222-2-2-2-22222-2-20000-22-22-22-220000000-2202-2000000000000000000
χ252222-2-2-2-222-2-22200002-22-2-22-22000000200-2002-200000000000000002222-2-2-2-222-2-22200002-22-2-22-22000000200-2002-20000000000000000
χ262222-2-2-2-222-2-22200002-22-2-22-22000000-200200-2200000000000000002222-2-2-2-222-2-22200002-22-2-22-22000000-200200-220000000000000000
χ272222-2-2-2-222-2-2220000-22-222-22-2000000200-200-2200000000000000002222-2-2-2-222-2-2220000-22-222-22-2000000200-200-220000000000000000
χ282222-2-2-2-222-2-2220000-22-222-22-2000000-2002002-200000000000000002222-2-2-2-222-2-2220000-22-222-22-2000000-2002002-20000000000000000
χ292-2-2222-2-22-22-22-2000022-2-22-2-2200000000000000002i−2i002i−2i000000002-2-2222-2-22-22-22-2000022-2-22-2-2200000000000000002i−2i002i−2i00000000
χ302-2-2222-2-22-22-22-2000022-2-22-2-220000000000000000−2i2i00−2i2i000000002-2-2222-2-22-22-22-2000022-2-22-2-220000000000000000−2i2i00−2i2i00000000
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χ322-2-2222-2-22-22-22-20000-2-222-222-20000000000000000-22002-2000000002-2-2222-2-22-22-22-20000-2-222-222-20000000000000000-22002-200000000
χ332-2-2222-2-22-2-22-22000022-2-2-222-2000000000000002i−2i002i−2i00000000002-2-2222-2-22-2-22-22000022-2-2-222-2000000000000002i−2i002i−2i0000000000
χ342-2-2222-2-22-2-22-22000022-2-2-222-200000000000000−2i2i00−2i2i00000000002-2-2222-2-22-2-22-22000022-2-2-222-200000000000000−2i2i00−2i2i0000000000
χ352-2-2222-2-22-2-22-220000-2-2222-2-22000000000000002-200-2200000000002-2-2222-2-22-2-22-220000-2-2222-2-22000000000000002-200-220000000000
χ362-2-2222-2-22-2-22-220000-2-2222-2-2200000000000000-22002-200000000002-2-2222-2-22-2-22-220000-2-2222-2-2200000000000000-22002-20000000000
χ372-2-22-2-2222-22-2-2200002-2-2222-2-200000000000000000000002i−2i002i−2i002-2-22-2-2222-22-2-2200002-2-2222-2-200000000000000000000002i−2i002i−2i00
χ382-2-22-2-2222-22-2-2200002-2-2222-2-20000000000000000000000−2i2i00−2i2i002-2-22-2-2222-22-2-2200002-2-2222-2-20000000000000000000000−2i2i00−2i2i00
χ392-2-22-2-2222-22-2-220000-222-2-2-22200000000000000000000002-200-22002-2-22-2-2222-22-2-220000-222-2-2-22200000000000000000000002-200-2200
χ402-2-22-2-2222-22-2-220000-222-2-2-2220000000000000000000000-22002-2002-2-22-2-2222-22-2-220000-222-2-2-2220000000000000000000000-22002-200
χ412-2-22-2-2222-2-222-200002-2-22-2-2220000000000000000000000002-2002-22-2-22-2-2222-2-222-200002-2-22-2-2220000000000000000000000002-2002-2
χ422-2-22-2-2222-2-222-200002-2-22-2-222000000000000000000000000-2200-222-2-22-2-2222-2-222-200002-2-22-2-222000000000000000000000000-2200-22
χ432-2-22-2-2222-2-222-20000-222-222-2-20000000000000000000000002i−2i00−2i2i2-2-22-2-2222-2-222-20000-222-222-2-20000000000000000000000002i−2i00−2i2i
χ442-2-22-2-2222-2-222-20000-222-222-2-2000000000000000000000000−2i2i002i−2i2-2-22-2-2222-2-222-20000-222-222-2-2000000000000000000000000−2i2i002i−2i
χ4544444-44-4-4-4000000000000000000004-400000000000000000000000044444-44-4-4-4000000000000000000004-4000000000000000000000000
χ4644444-44-4-4-400000000000000000000-4400000000000000000000000044444-44-4-4-400000000000000000000-44000000000000000000000000
χ474444-44-44-4-40000000000000000004-4000000000000000000000000004444-44-44-4-40000000000000000004-400000000000000000000000000
χ484444-44-44-4-4000000000000000000-44000000000000000000000000004444-44-44-4-4000000000000000000-4400000000000000000000000000
χ494-4-444-4-44-4400000000000000004-400000000000000000000000000004-4-444-4-44-4400000000000000004-40000000000000000000000000000
χ504-4-444-4-44-440000000000000000-4400000000000000000000000000004-4-444-4-44-440000000000000000-440000000000000000000000000000
χ514-4-44-444-4-44000044-4-4000000000000000000000000000000000000004-4-44-444-4-44000044-4-400000000000000000000000000000000000000
χ524-4-44-444-4-440000-4-444000000000000000000000000000000000000004-4-44-444-4-440000-4-44400000000000000000000000000000000000000
χ5388-8-800000000004-44-40000000000000000000000000000000000000088-8-800000000004-44-400000000000000000000000000000000000000
χ5488-8-80000000000-44-440000000000000000000000000000000000000088-8-80000000000-44-4400000000000000000000000000000000000000
χ558-88-800000000004-4-44000000000000000000000000000000000000008-88-800000000004-4-4400000000000000000000000000000000000000
χ568-88-80000000000-444-4000000000000000000000000000000000000008-88-80000000000-444-400000000000000000000000000000000000000
χ5711111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ581111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111
χ5911111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ6011111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ61111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11-1-1111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-111-1-1-111−i−i−i−iiiii−i−i−i−iiiii
χ62111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11-1-1111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-111-1-1-111iiii−i−i−i−iiiii−i−i−i−i
χ63111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1-111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111-1-1111-1-1−i−i−i−iiiiiiiii−i−i−i−i
χ64111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111-1-1111-1-1iiii−i−i−i−i−i−i−i−iiiii
χ6511111111111111-1-1-1-111111111-1-1-1-1-1-11-1-11-1-11111-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-111-111-1-1-1-111-1-111-1-111-1-111
χ6611111111111111-1-1-1-111111111-1-1-1-1-1-11-1-11-1-111-1-111-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-111-111-1-111-1-111-1-111-1-111-1-1
χ6711111111111111-1-1-1-111111111-1-1-1-1-1-1-111-111-1-111-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111-1-11-1-111-1-111-1-11111-1-111-1-1
χ6811111111111111-1-1-1-111111111-1-1-1-1-1-1-111-111-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111-1-11-1-11111-1-111-1-1-1-111-1-111
χ6911111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1ii−i−i−i−iiiii−i−i−i−iii-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i
χ7011111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1−i−iiiii−i−i−i−iiiii−i−i-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii
χ7111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111ii−i−i−i−iii−i−iiiii−i−i-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1−i−iiiii−i−iii−i−i−i−iii
χ7211111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111−i−iiiii−i−iii−i−i−i−iii-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i
χ732222222222-2-2-2-222222222-2-2-2-2-2-222-2-2000000000000000000000000-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2222222-2-222000000000000000000000000
χ742222222222-2-2-2-22222-2-2-2-22222-2-2-2-222000000000000000000000000-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-22222-2-2000000000000000000000000
χ752222222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-222000000000000000000000000-2-2-2-2-2-2-2-2-2-222222222-2-2-2-22222-2-222-2-2000000000000000000000000
χ762222222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2000000000000000000000000-2-2-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-222000000000000000000000000
χ772222-2-2-2-22222-2-200002-22-22-22-200000002-202-2000000000000000000-2-2-2-22222-2-2-2-2220000-22-22-22-220000000-220-22000000000000000000
χ782222-2-2-2-22222-2-200002-22-22-22-20000000-220-22000000000000000000-2-2-2-22222-2-2-2-2220000-22-22-22-2200000002-202-2000000000000000000
χ792222-2-2-2-22222-2-20000-22-22-22-2200000002-20-22000000000000000000-2-2-2-22222-2-2-2-22200002-22-22-22-20000000-2202-2000000000000000000
χ802222-2-2-2-22222-2-20000-22-22-22-220000000-2202-2000000000000000000-2-2-2-22222-2-2-2-22200002-22-22-22-200000002-20-22000000000000000000
χ812222-2-2-2-222-2-22200002-22-2-22-22000000200-2002-20000000000000000-2-2-2-22222-2-222-2-20000-22-222-22-2000000-200200-220000000000000000
χ822222-2-2-2-222-2-22200002-22-2-22-22000000-200200-220000000000000000-2-2-2-22222-2-222-2-20000-22-222-22-2000000200-2002-20000000000000000
χ832222-2-2-2-222-2-2220000-22-222-22-2000000200-200-220000000000000000-2-2-2-22222-2-222-2-200002-22-2-22-22000000-2002002-20000000000000000
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χ872-2-2222-2-22-22-22-20000-2-222-222-200000000000000002-200-2200000000-222-2-2-222-22-22-22000022-2-22-2-220000000000000000-22002-200000000
χ882-2-2222-2-22-22-22-20000-2-222-222-20000000000000000-22002-200000000-222-2-2-222-22-22-22000022-2-22-2-2200000000000000002-200-2200000000
χ892-2-2222-2-22-2-22-22000022-2-2-222-2000000000000002i−2i002i−2i0000000000-222-2-2-222-222-22-20000-2-2222-2-2200000000000000−2i2i00−2i2i0000000000
χ902-2-2222-2-22-2-22-22000022-2-2-222-200000000000000−2i2i00−2i2i0000000000-222-2-2-222-222-22-20000-2-2222-2-22000000000000002i−2i002i−2i0000000000
χ912-2-2222-2-22-2-22-220000-2-2222-2-22000000000000002-200-220000000000-222-2-2-222-222-22-2000022-2-2-222-200000000000000-22002-20000000000
χ922-2-2222-2-22-2-22-220000-2-2222-2-2200000000000000-22002-20000000000-222-2-2-222-222-22-2000022-2-2-222-2000000000000002-200-220000000000
χ932-2-22-2-2222-22-2-2200002-2-2222-2-200000000000000000000002i−2i002i−2i00-222-222-2-2-22-222-20000-222-2-2-2220000000000000000000000−2i2i00−2i2i00
χ942-2-22-2-2222-22-2-2200002-2-2222-2-20000000000000000000000−2i2i00−2i2i00-222-222-2-2-22-222-20000-222-2-2-22200000000000000000000002i−2i002i−2i00
χ952-2-22-2-2222-22-2-220000-222-2-2-22200000000000000000000002-200-2200-222-222-2-2-22-222-200002-2-2222-2-20000000000000000000000-22002-200
χ962-2-22-2-2222-22-2-220000-222-2-2-2220000000000000000000000-22002-200-222-222-2-2-22-222-200002-2-2222-2-200000000000000000000002-200-2200
χ972-2-22-2-2222-2-222-200002-2-22-2-2220000000000000000000000002-2002-2-222-222-2-2-222-2-220000-222-222-2-2000000000000000000000000-2200-22
χ982-2-22-2-2222-2-222-200002-2-22-2-222000000000000000000000000-2200-22-222-222-2-2-222-2-220000-222-222-2-20000000000000000000000002-2002-2
χ992-2-22-2-2222-2-222-20000-222-222-2-20000000000000000000000002i−2i00−2i2i-222-222-2-2-222-2-2200002-2-22-2-222000000000000000000000000−2i2i002i−2i
χ1002-2-22-2-2222-2-222-20000-222-222-2-2000000000000000000000000−2i2i002i−2i-222-222-2-2-222-2-2200002-2-22-2-2220000000000000000000000002i−2i00−2i2i
χ10144444-44-4-4-4000000000000000000004-4000000000000000000000000-4-4-4-4-44-444400000000000000000000-44000000000000000000000000
χ10244444-44-4-4-400000000000000000000-44000000000000000000000000-4-4-4-4-44-4444000000000000000000004-4000000000000000000000000
χ1034444-44-44-4-40000000000000000004-400000000000000000000000000-4-4-4-44-44-444000000000000000000-4400000000000000000000000000
χ1044444-44-44-4-4000000000000000000-4400000000000000000000000000-4-4-4-44-44-4440000000000000000004-400000000000000000000000000
χ1054-4-444-4-44-4400000000000000004-40000000000000000000000000000-444-4-444-44-40000000000000000-440000000000000000000000000000
χ1064-4-444-4-44-440000000000000000-440000000000000000000000000000-444-4-444-44-400000000000000004-40000000000000000000000000000
χ1074-4-44-444-4-44000044-4-400000000000000000000000000000000000000-444-44-4-444-40000-4-44400000000000000000000000000000000000000
χ1084-4-44-444-4-440000-4-44400000000000000000000000000000000000000-444-44-4-444-4000044-4-400000000000000000000000000000000000000
χ10988-8-800000000004-44-400000000000000000000000000000000000000-8-8880000000000-44-4400000000000000000000000000000000000000
χ11088-8-80000000000-44-4400000000000000000000000000000000000000-8-88800000000004-44-400000000000000000000000000000000000000
χ1118-88-800000000004-4-4400000000000000000000000000000000000000-88-880000000000-444-400000000000000000000000000000000000000
χ1128-88-80000000000-444-400000000000000000000000000000000000000-88-8800000000004-4-4400000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).