Finite Group Databasebeta

← Group #72318119

Character table — Group #72318119

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size112222222444444444444888888888888888816161616161616161616161616161616161616161616161616161616161632323232323232323232323232323232323232323232323232323232323232646464646464
order12222222222224444444422222244444444442222222244444444444444444444444444444444444444444888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-1111-1-1-1-111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111-1-1-1-1111-1-1-1-11111111-1-1-1-1-1-1-1-111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111
χ51111111111111111111-1-111-1-1-1-11111111-1-1-11-1-1-1111111-111111-1-1-1-1-1-1iiii−i−i−i−i1-111111ii−i−iiiii−i−i−i−i-1-1-1-1iiii−i−i−i−i-1-1ii−i−i
χ61111111111111111111-1-111-1-1-1-11111111-1-1-11-1-1-1111111-111111-1-1-1-1-1-1−i−i−i−iiiii1-111111−i−iii−i−i−i−iiiii-1-1-1-1−i−i−i−iiiii-1-1−i−iii
χ71111111111111111111-1-111-1-1-1-11111111-1-1-11-1-1-1-1-1-1-111-1-1-1-1-11-1-1-1-1-1-1iiii−i−i−i−i1-1-1-1-1-11ii−i−iiiii−i−i−i−i1111−i−i−i−iiiii11−i−iii
χ81111111111111111111-1-111-1-1-1-11111111-1-1-11-1-1-1-1-1-1-111-1-1-1-1-11-1-1-1-1-1-1−i−i−i−iiiii1-1-1-1-1-11−i−iii−i−i−i−iiiii1111iiii−i−i−i−i11ii−i−i
χ911111111111-1-1111111111-1111111111-1-111111-1-111111-111111-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1111111111111-1-1-1-1-1-1
χ1011111111111-1-1111111111-1111111111-1-111111-1-111111-111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-11111
χ1111111111111-1-1111111111-1111111111-1-111111-1-1-1-1-1-11-11-1-1-1-1-111-1-1-1-111111111-1-11111-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ1211111111111-1-1111111111-1111111111-1-111111-1-1-1-1-1-11-11-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-111-1-111-1-1-1-11111111111-1-1-1-1
χ1311111111111-1-1111111-1-11-1-1-1-1-111111-1-1-1-1-11-11111111-1-11111-1-1-11111iiii−i−i−i−i-11-1-1-1-1-1−i−iiiii−i−i−i−iii-1-1-1-1iiii−i−i−i−i11−i−iii
χ1411111111111-1-1111111-1-11-1-1-1-1-111111-1-1-1-1-11-11111111-1-11111-1-1-11111−i−i−i−iiiii-11-1-1-1-1-1ii−i−i−i−iiiii−i−i-1-1-1-1−i−i−i−iiiii11ii−i−i
χ1511111111111-1-1111111-1-11-1-1-1-1-111111-1-1-1-1-11-111-1-1-1-11-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i-111111-1−i−iiiii−i−i−i−iii1111−i−i−i−iiiii-1-1ii−i−i
χ1611111111111-1-1111111-1-11-1-1-1-1-111111-1-1-1-1-11-111-1-1-1-11-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii-111111-1ii−i−i−i−iiiii−i−i1111iiii−i−i−i−i-1-1−i−iii
χ17111111111-1-1111-1-111111-1111111111-1-1-1111-1-11111-1-1-11-111-1-1-1-1-111-1-1111111111-111-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-111-1-11-11-11-1
χ18111111111-1-1111-1-111111-1111111111-1-1-1111-1-11111-1-1-11-111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11-111-1-1-1111111-1-111-1-111-1-1-1-111-1-1111-1-11-11
χ19111111111-1-1111-1-111111-1111111111-1-1-1111-1-111-1-111-11-1-1-111-1-1-111-1-1111111111-1-1-111-1-1-1-1-1-1-111-1-111-1-111-1-111-1-111-11-11-11
χ20111111111-1-1111-1-111111-1111111111-1-1-1111-1-111-1-111-11-1-1-111-1-1-111-1-1-1-1-1-1-1-1-1-11-1-1-111-1111111-1-111-1-1-1-11111-1-111-1-1-111-11-1
χ21111111111-1-1111-1-1111-1-1-11-1-1-1-11111-1-1-1-1-1-1-11-1-111-1-1-11111-1-1-111-1-111iiii−i−i−i−i1111-1-1-1−i−iii−i−iiiii−i−i-1-111ii−i−i−i−iii-11i−i−ii
χ22111111111-1-1111-1-1111-1-1-11-1-1-1-11111-1-1-1-1-1-1-11-1-111-1-1-11111-1-1-111-1-111−i−i−i−iiiii1111-1-1-1ii−i−iii−i−i−i−iii-1-111−i−iiiii−i−i-11−iii−i
χ23111111111-1-1111-1-1111-1-1-11-1-1-1-11111-1-1-1-1-1-1-11-1-1-1-111-111-1-111-111-1-111iiii−i−i−i−i11-1-111-1−i−iii−i−iiiii−i−i11-1-1−i−iiiii−i−i1-1−iii−i
χ24111111111-1-1111-1-1111-1-1-11-1-1-1-11111-1-1-1-1-1-1-11-1-1-1-111-111-1-111-111-1-111−i−i−i−iiiii11-1-111-1ii−i−iii−i−i−i−iii11-1-1ii−i−i−i−iii1-1i−i−ii
χ25111111111-1-1-1-11-1-111111-1-111111111-111111-1-1-1-111-1-1-1-1-111-1-11-1-1-1-11111111111-11-1-11111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1-11-11-11
χ26111111111-1-1-1-11-1-111111-1-111111111-111111-1-1-1-111-1-1-1-1-111-1-11-1-1-1-111-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-11111111111-1-1-1-111-1-111-111-11-1
χ27111111111-1-1-1-11-1-111111-1-111111111-111111-1-1-1-1-1-111-1-1-1-1-1111-1-1-1-11111111111-1111-1-111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1111-11-11-1
χ28111111111-1-1-1-11-1-111111-1-111111111-111111-1-1-1-1-1-111-1-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1111-1-11-1-1-1-111111111-1-11111-1-111-1-11-1-11-11
χ29111111111-1-1-1-11-1-1111-1-1-1-1-1-1-1-11111-111-1-1-1-111111-1-1-1-1111-1-111111-1-1iiii−i−i−i−i-1-1-1-1111ii−i−i−i−i−i−iiiii-1-111ii−i−i−i−iii1-1−iii−i
χ30111111111-1-1-1-11-1-1111-1-1-1-1-1-1-1-11111-111-1-1-1-111111-1-1-1-1111-1-111111-1-1−i−i−i−iiiii-1-1-1-1111−i−iiiiiii−i−i−i−i-1-111−i−iiiii−i−i1-1i−i−ii
χ31111111111-1-1-1-11-1-1111-1-1-1-1-1-1-1-11111-111-1-1-1-1111-1-111-1-11-1-11111111-1-1iiii−i−i−i−i-1-111-1-11ii−i−i−i−i−i−iiiii11-1-1−i−iiiii−i−i-11i−i−ii
χ32111111111-1-1-1-11-1-1111-1-1-1-1-1-1-1-11111-111-1-1-1-1111-1-111-1-11-1-11111111-1-1−i−i−i−iiiii-1-111-1-11−i−iiiiiii−i−i−i−i11-1-1ii−i−i−i−iii-11−iii−i
χ3322222222222222222222222-2-2-2-2-2-2-2-2222222-2-2-2-20000-22-2000022222-2-200000000-220000-2000000000000000000000000000000
χ342222222222222222222-2-2222222-2-2-2-2222-2-2-2-22220000-22200002-2-2-2-22200000000-2-20000-2000000000000000000000000000000
χ3522222222222-2-2222222222-2-2-2-2-2-2-2-2-22-2-2222-2-2220000-2-2-20000-222-2-222000000002-200002000000000000000000000000000000
χ3622222222222-2-2222222-2-22-22222-2-2-2-22-2-2-2-2-2-22-2-20000-2-220000-2-2-222-2-2000000002200002000000000000000000000000000000
χ37222222222-2-2222-2-222222-22-2-2-2-2-2-2-2-2-2-2-222222-2-200002220000-2-2-2222200000000-2-200002000000000000000000000000000000
χ38222222222-2-2222-2-2222-2-2-222222-2-2-2-2-2-2-2-2-2-22-222000022-20000-222-2-2-2-200000000-2200002000000000000000000000000000000
χ39222222222-2-2-2-22-2-222222-2-2-2-2-2-2-2-2-2-2-222222222200002-2200002-2-2-2-2-2-200000000220000-2000000000000000000000000000000
χ40222222222-2-2-2-22-2-2222-2-2-2-22222-2-2-2-2-222-2-2-22-2-2-200002-2-200002222222000000002-20000-2000000000000000000000000000000
χ41222-2-22-22-20000-2002-2222002-2-2222-2-2000-22-20000002-2000002-2000000022-2-222-2-20000000000000000000002-2002-2002-2000000
χ42222-2-22-22-20000-2002-2222002-2-2222-2-2000-22-20000002-2000002-20000000-2-222-2-2220000000000000000000002-200-2200-22000000
χ43222-2-22-22-20000-2002-2222002-2-2222-2-2000-22-2000000-2200000-22000000022-2-222-2-2000000000000000000000-2200-2200-22000000
χ44222-2-22-22-20000-2002-2222002-2-2222-2-2000-22-2000000-2200000-220000000-2-222-2-222000000000000000000000-22002-2002-2000000
χ45222-2-22-22-20000-2002-22-2-200-222-222-2-20002-220000002-2000002-200000002i2i−2i−2i−2i−2i2i2i000000000000000000000-22002i−2i00−2i2i000000
χ46222-2-22-22-20000-2002-22-2-200-222-222-2-20002-220000002-2000002-20000000−2i−2i2i2i2i2i−2i−2i000000000000000000000-2200−2i2i002i−2i000000
χ47222-2-22-22-20000-2002-22-2-200-222-222-2-20002-22000000-2200000-2200000002i2i−2i−2i−2i−2i2i2i0000000000000000000002-200−2i2i002i−2i000000
χ48222-2-22-22-20000-2002-22-2-200-222-222-2-20002-22000000-2200000-220000000−2i−2i2i2i2i2i−2i−2i0000000000000000000002-2002i−2i00−2i2i000000
χ4922-22-2-222-20000-200-2222200-22-222-22-2000-2-2200002-2000002-20000000002-22-22-22-200000000000000000002-2002-2002-200000000
χ5022-22-2-222-20000-200-2222200-22-222-22-2000-2-2200002-2000002-2000000000-22-22-22-2200000000000000000002-200-2200-2200000000
χ5122-22-2-222-20000-200-2222200-22-222-22-2000-2-220000-2200000-220000000002-22-22-22-20000000000000000000-2200-2200-2200000000
χ5222-22-2-222-20000-200-2222200-22-222-22-2000-2-220000-2200000-22000000000-22-22-22-220000000000000000000-22002-2002-200000000
χ5322-22-2-222-20000-200-222-2-2002-22-22-22-200022-200002-2000002-20000000002i−2i2i−2i−2i2i−2i2i0000000000000000000-22002i−2i00−2i2i00000000
χ5422-22-2-222-20000-200-222-2-2002-22-22-22-200022-200002-2000002-2000000000−2i2i−2i2i2i−2i2i−2i0000000000000000000-2200−2i2i002i−2i00000000
χ5522-22-2-222-20000-200-222-2-2002-22-22-22-200022-20000-2200000-220000000002i−2i2i−2i−2i2i−2i2i00000000000000000002-200−2i2i002i−2i00000000
χ5622-22-2-222-20000-200-222-2-2002-22-22-22-200022-20000-2200000-22000000000−2i2i−2i2i2i−2i2i−2i00000000000000000002-2002i−2i00−2i2i00000000
χ5722-2-22-2-22222002-2-2-2-2222-2022-2-2-222-22002-2-22-2000000-202000002-200000000000000000002i−2i2i−2i002i−2i002i−2i000000000000000000
χ5822-2-22-2-22222002-2-2-2-2222-2022-2-2-222-22002-2-22-2000000-202000002-20000000000000000000−2i2i−2i2i00−2i2i00−2i2i000000000000000000
χ5922-2-22-2-22222002-2-2-2-2222-20-2-2222-2-222002-2-2-2200000020-2000002-200002-2-222-2-22000000000002-2002-200000000000000000000
χ6022-2-22-2-22222002-2-2-2-2222-20-2-2222-2-222002-2-2-2200000020-2000002-20000-222-2-222-200000000000-2200-2200000000000000000000
χ6122-2-22-2-22222002-2-2-2-22-2-2-2022-2-22-2-22200-222-2-200000020200000-2200002i−2i−2i2i−2i2i2i−2i000000000002i−2i00−2i2i00000000000000000000
χ6222-2-22-2-22222002-2-2-2-22-2-2-2022-2-22-2-22200-222-2-200000020200000-220000−2i2i2i−2i2i−2i−2i2i00000000000−2i2i002i−2i00000000000000000000
χ6322-2-22-2-22222002-2-2-2-22-2-2-20-2-222-222-2200-22222000000-20-200000-2200000000000000000002-2-22002-200-22000000000000000000
χ6422-2-22-2-22222002-2-2-2-22-2-2-20-2-222-222-2200-22222000000-20-200000-220000000000000000000-222-200-22002-2000000000000000000
χ6522-2-22-2-222-2-200222-2-22222022-2-2-222-2-2002-2-2-2200000020-200000-2200000000000000000002i−2i2i−2i00−2i2i00−2i2i000000000000000000
χ6622-2-22-2-222-2-200222-2-22222022-2-2-222-2-2002-2-2-2200000020-200000-220000000000000000000−2i2i−2i2i002i−2i002i−2i000000000000000000
χ6722-2-22-2-222-2-200222-2-222220-2-2222-2-22-2002-2-22-2000000-20200000-2200002-2-222-2-2200000000000-2200-2200000000000000000000
χ6822-2-22-2-222-2-200222-2-222220-2-2222-2-22-2002-2-22-2000000-20200000-220000-222-2-222-2000000000002-2002-200000000000000000000
χ6922-2-22-2-222-2-200222-2-22-2-22022-2-22-2-22-200-22222000000-20-2000002-200002i−2i−2i2i−2i2i2i−2i00000000000−2i2i002i−2i00000000000000000000
χ7022-2-22-2-222-2-200222-2-22-2-22022-2-22-2-22-200-22222000000-20-2000002-20000−2i2i2i−2i2i−2i−2i2i000000000002i−2i00−2i2i00000000000000000000
χ7122-2-22-2-222-2-200222-2-22-2-220-2-222-222-2-200-222-2-2000000202000002-200000000000000000002-2-2200-22002-2000000000000000000
χ7222-2-22-2-222-2-200222-2-22-2-220-2-222-222-2-200-222-2-2000000202000002-20000000000000000000-222-2002-200-22000000000000000000
χ734444444444444-444-4-4-400-4400000000-444000000000000-400000-4000000000000000000000000000000000000000000000000000
χ7444444444444-4-4-444-4-4-400-4-400000000-4-4-40000000000004000004000000000000000000000000000000000000000000000000000
χ75444444444-4-444-4-4-4-4-4-40044000000004-4-4000000000000-4000004000000000000000000000000000000000000000000000000000
χ76444444444-4-4-4-4-4-4-4-4-4-4004-400000000444000000000000400000-4000000000000000000000000000000000000000000000000000
χ77444-4-44-44-40000-4004-444400-444-4-4-444000-44-40000000000000000000000000000000000000000000000000000000000000000000
χ78444-4-44-44-40000-4004-44-4-4004-4-44-4-4440004-440000000000000000000000000000000000000000000000000000000000000000000
χ7944-44-4-444-40000-400-44444004-44-4-44-44000-4-440000000000000000000000000000000000000000000000000000000000000000000
χ8044-44-4-444-40000-400-444-4-400-44-44-44-4400044-40000000000000000000000000000000000000000000000000000000000000000000
χ8144-4-44-4-4444400-4-4-444-4004000000000-400000004-400000000000000004-4000000000000000000000000000000000000000000000
χ8244-4-44-4-4444400-4-4-444-4004000000000-40000000-440000000000000000-44000000000000000000000000000000000000000000000
χ8344-4-44-4-444-4-400-44444-400-4000000000400000004-40000000000000000-44000000000000000000000000000000000000000000000
χ8444-4-44-4-444-4-400-44444-400-400000000040000000-4400000000000000004-4000000000000000000000000000000000000000000000
χ8544-4-4-444-444-44404-4000000-40000000004-400000002-22-2000-22-22000000000000000002-22-20000000000000000000000000000000
χ8644-4-4-444-444-44404-4000000-40000000004-40000000-22-220002-22-200000000000000000-22-220000000000000000000000000000000
χ8744-4-4-444-444-4-4-404-40000004000000000-4400000002-22-2000-22-2200000000000000000-22-220000000000000000000000000000000
χ8844-4-4-444-444-4-4-404-40000004000000000-440000000-22-220002-22-2000000000000000002-22-20000000000000000000000000000000
χ8944-4-4-444-44-44440-44000000-4000000000-4400000002-2-22000-222-2000000000000000002-2-220000000000000000000000000000000
χ9044-4-4-444-44-44440-44000000-4000000000-440000000-222-20002-2-2200000000000000000-222-20000000000000000000000000000000
χ9144-4-4-444-44-44-4-40-4400000040000000004-400000002-2-22000-222-200000000000000000-222-20000000000000000000000000000000
χ9244-4-4-444-44-44-4-40-4400000040000000004-40000000-222-20002-2-22000000000000000002-2-220000000000000000000000000000000
χ938888-8-8-8-888-8000-880000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ948888-8-8-8-88-880008-80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ95888-88-88-8-8000000000000000000000000000000004400000-4-4000000000000000000000000000000000000000000000000000000
χ96888-88-88-8-800000000000000000000000000000000-4-40000044000000000000000000000000000000000000000000000000000000
χ97888-8-88-88-80000800-88-80000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9888-8888-8-8-800000000000000000000000000000000004400000-4-40000000000000000000000000000000000000000000000000000
χ9988-8888-8-8-80000000000000000000000000000000000-4-400000440000000000000000000000000000000000000000000000000000
χ10088-88-8-888-800008008-8-80000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10116-160000000008-80000008i−8i00000000000000000000000000000000004i−4i00000000000000000000000000000000000000000000000
χ10216-160000000008-8000000−8i8i0000000000000000000000000000000000−4i4i00000000000000000000000000000000000000000000000
χ10316-16000000000-880000008i−8i0000000000000000000000000000000000−4i4i00000000000000000000000000000000000000000000000
χ10416-16000000000-88000000−8i8i00000000000000000000000000000000004i−4i00000000000000000000000000000000000000000000000

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