Finite Group Databasebeta

← Group #72258813

Character table — Group #72258813

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222222222444444444444444444444488888888888812121212121212121212121212121212161616161616161616161616161616161616161616162424242432323232323248484848484848484848
order122222344446668888888844446688881212121224242424242424244444121212122424242488888888888888888812121212161616162424242448484848484848482244441212121244448816161616
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1
χ511111111111111111111111111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1
χ611111111111111111111111111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ711111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-11111
χ811111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111
χ911-1-11-11-11-111-1-111-1-111-1-1-1-1111-11-11-1-111-111-1-1-1-111ii−i−i11-1-111-1-111111111-1-1-1-1-1-1-1-1i−iii−i−i11-1-1ii−i−i1111-1-1-1-11-11-1i−iii−i−iii−i−i1-1ii−i−i
χ1011-1-11-11-11-111-1-111-1-111-1-1-1-1111-11-11-1-111-111-1-1-1-111ii−i−i11-1-111-1-111111111-1-1-1-1-1-1-1-1i−iii−i−i-1-111ii−i−i-1-1-1-11111-11-11−ii−i−iii−i−iii-11ii−i−i
χ1111-1-11-11-11-111-1-111-1-111-1-1-1-1111-11-11-1-111-111-1-1-1-111ii−i−i11-1-111-1-1-1-1-1-1-1-1-1-111111111i−iii−i−i11-1-1ii−i−i1111-1-1-1-1-11-11i−iii−i−i−i−iii-11−i−iii
χ1211-1-11-11-11-111-1-111-1-111-1-1-1-1111-11-11-1-111-111-1-1-1-111ii−i−i11-1-111-1-1-1-1-1-1-1-1-1-111111111i−iii−i−i-1-111ii−i−i-1-1-1-111111-11-1−ii−i−iiiii−i−i1-1−i−iii
χ1311-1-11-11-11-111-1-111-1-111-1-1-1-1111-11-11-1-111-111-1-1-1-111−i−iii11-1-111-1-111111111-1-1-1-1-1-1-1-1−ii−i−iii11-1-1−i−iii1111-1-1-1-11-11-1−ii−i−iii−i−iii1-1−i−iii
χ1411-1-11-11-11-111-1-111-1-111-1-1-1-1111-11-11-1-111-111-1-1-1-111−i−iii11-1-111-1-111111111-1-1-1-1-1-1-1-1−ii−i−iii-1-111−i−iii-1-1-1-11111-11-11i−iii−i−iii−i−i-11−i−iii
χ1511-1-11-11-11-111-1-111-1-111-1-1-1-1111-11-11-1-111-111-1-1-1-111−i−iii11-1-111-1-1-1-1-1-1-1-1-1-111111111−ii−i−iii11-1-1−i−iii1111-1-1-1-1-11-11−ii−i−iiiii−i−i-11ii−i−i
χ1611-1-11-11-11-111-1-111-1-111-1-1-1-1111-11-11-1-111-111-1-1-1-111−i−iii11-1-111-1-1-1-1-1-1-1-1-1-111111111−ii−i−iii-1-111−i−iii-1-1-1-111111-11-1i−iii−i−i−i−iii1-1ii−i−i
χ172222222222222222-2-2-2-222-2-2-2-22222-2-222222222-2-2-2-20000-2-2-2-22-22-20000000000000000000000000000000000000022220000000000-2-20000
χ182222222222222222-2-2-2-222-2-2-2-22222-2-222222222-2-2-2-20000-2-2-2-22-22-200000000000000000000000000000000000000-2-2-2-20000000000220000
χ1922222222222222-2-22222-2-2-2-2-2-222-2-2222222-2-2-2-222222222-2-2-2-2-22-220000000000000000-2-222220000-2-2-2-20000000000000000000000000000
χ2022222222222222-2-22222-2-2-2-2-2-222-2-2222222-2-2-2-22222-2-2-2-2-2-2-2-2-22-22000000000000000022-2-2-2-2000022220000000000000000000000000000
χ2122222222222222-2-2-2-2-2-2-2-2222222-2-2-2-22222-2-2-2-2-2-2-2-200002222-2-2-2-20000000000000000000000000000000000000000000000002-22-2000000
χ2222222222222222-2-2-2-2-2-2-2-2222222-2-2-2-22222-2-2-2-2-2-2-2-200002222-2-2-2-2000000000000000000000000000000000000000000000000-22-22000000
χ23222222-12222-1-1-1222222222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000000022-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-10000000000
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χ25222222-12222-1-1-1222222222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-10000000000000000-2-2111122221111-1-1-1-1-1-1-1-10000-2-211110000000000
χ26222222-12222-1-1-1222222222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-10000000000000000-2-21111-2-2-2-2111111111111000022-1-1-1-10000000000
χ27222222-12222-1-1-1-2-22222-2-2-2-2-2-2-1-1-2-222-1-1-1-11111-1-1-1-1222211111-11-10000000000000000-2-2-1-1-1-100001111−i3−i3i3i3−i3−i3i3i3000000−i3i3−i3i30000000000
χ28222222-12222-1-1-1-2-22222-2-2-2-2-2-2-1-1-2-222-1-1-1-11111-1-1-1-1222211111-11-10000000000000000-2-2-1-1-1-100001111i3i3−i3−i3i3i3−i3−i3000000i3−i3i3−i30000000000
χ29222222-12222-1-1-1-2-22222-2-2-2-2-2-2-1-1-2-222-1-1-1-11111-1-1-1-1-2-2-2-211111-11-100000000000000002211110000-1-1-1-1−i3−i3i3i3−i3−i3i3i3000000i3−i3i3−i30000000000
χ30222222-12222-1-1-1-2-22222-2-2-2-2-2-2-1-1-2-222-1-1-1-11111-1-1-1-1-2-2-2-211111-11-100000000000000002211110000-1-1-1-1i3i3−i3−i3i3i3−i3−i3000000−i3i3−i3i30000000000
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χ332222-2-222-2-2222200-2-2-2-2000000-2-2002222-2-20000-2-2-2-2-22-2200000202−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i200-22-2200000000000000000000000000000000i2−i2i2−i2
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χ4022-2-22-22-22-222-2-22222-2-2-2-222-2-22-22-2-22-222-222-2-222-2-20000-2-2222-2-2200000000000000000000000000000000000000-22-2200000000002-20000
χ4122-2-22-22-22-222-2-2-2-222-2-222-2-2222-2-22-22-222-2-2-22222-2-2000022-2-2-2-2220000000000000000000000000000000000000000000000002i−2i−2i2i000000
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χ4322-2-22-22-22-222-2-2-2-2-2-2222222-2-22-2-222-2-222-2-2-222-2-2222i2i−2i−2i-2-222-222-20000000000000000−2i2i2i2i−2i−2i0000−2i−2i2i2i0000000000000000000000000000
χ4422-2-22-22-22-222-2-2-2-2-2-2222222-2-22-2-222-2-222-2-2-222-2-222−2i−2i2i2i-2-222-222-200000000000000002i−2i−2i−2i2i2i00002i2i−2i−2i0000000000000000000000000000
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χ1088-88-800-400004-44−4i24i24i2−4i24i2−4i2−4i24i2-44-4400000000002i2−2i22i2−2i2−2i22i2−2i22i200002-22-200000000000000000000000000000000000000000000000000000000000000
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χ1108-88-800-400004-444i2−4i24i2−4i24i2−4i24i2−4i24-44-40000000000−2i22i2−2i22i2−2i22i2−2i22i20000-22-2200000000000000000000000000000000000000000000000000000000000000
χ1118-8-8800-4000044-4−4i24i2−4i24i24i2−4i24i2−4i24-4-4400000000002i2−2i2−2i22i22i2−2i2−2i22i200002-2-2200000000000000000000000000000000000000000000000000000000000000
χ1128-8-8800-4000044-4−4i24i24i2−4i2−4i24i24i2−4i2-444-400000000002i2−2i2−2i22i2−2i22i22i2−2i20000-222-200000000000000000000000000000000000000000000000000000000000000
χ1138-8-8800-4000044-44i2−4i2−4i24i24i2−4i2−4i24i2-444-40000000000−2i22i22i2−2i22i2−2i2−2i22i20000-222-200000000000000000000000000000000000000000000000000000000000000
χ1148-8-8800-4000044-44i2−4i24i2−4i2−4i24i2−4i24i24-4-440000000000−2i22i22i2−2i2−2i22i22i2−2i200002-2-2200000000000000000000000000000000000000000000000000000000000000

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