Finite Group Databasebeta

← Group #13140245

Character table — Group #13140245

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111222222224444446666666666666666121212121212121212121212121212121212121212121212181818181818181818181818363636363636363636363636363636363636363636363636363636363636
order12222222366666664412121212336666666666666636666666121212121212121212121212121212124444444444442222446666666612121212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ51111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111
χ61111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ71111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ81111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ9111-11-1-1-1111-1-1-11-1i−iii−i−i11111111-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i11-1-11-11-1i−i11-1-111-1-111-1-1ii−i−iii−i−iii−i−i
χ10111-11-1-1-1111-1-1-11-1i−iii−i−i11111111-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−i−i−iii-1-1111-1-11−ii11-1-1-1-111-1-111−i−iiiii−i−i−i−iii
χ11111-11-1-1-1111-1-1-11-1i−iii−i−i11111111-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iiiii−i−i-1-111-111-1−ii-1-11111-1-1-1-111−i−iii−i−iiiii−i−i
χ12111-11-1-1-1111-1-1-11-1i−iii−i−i11111111-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii11-1-1-11-11i−i-1-111-1-11111-1-1ii−i−i−i−iii−i−iii
χ13111-11-1-1-1111-1-1-11-1−ii−i−iii11111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i11-1-1-11-11−ii-1-111-1-11111-1-1−i−iiiii−i−iii−i−i
χ14111-11-1-1-1111-1-1-11-1−ii−i−iii11111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−i−i−iii-1-111-111-1i−i-1-11111-1-1-1-111ii−i−iii−i−i−i−iii
χ15111-11-1-1-1111-1-1-11-1−ii−i−iii11111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iiiii−i−i-1-1111-1-11i−i11-1-1-1-111-1-111ii−i−i−i−iiiii−i−i
χ16111-11-1-1-1111-1-1-11-1−ii−i−iii11111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii11-1-11-11-1−ii11-1-111-1-111-1-1−i−iii−i−iii−i−iii
χ1722222222222222222222222-1222-1-1-122-1-12-12-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-10000222200000022000000-1-1-1-1000000000000-1-1-1-1
χ1822222222222222222222222-1222-1-1-122-1-12-12-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-10000-2-2-2-2000000-2-200000011110000000000001111
χ192222222222222222222222-12-1-1-1222-1-122-12-12-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1222200000000220000-1-1-1-1000000000000-1-1-1-10000
χ202222222222222222222222-12-1-1-1222-1-122-12-12-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-2-2-2-200000000-2-20000111100000000000011110000
χ212222222222222222-2-2-2-2-2-22-1222-1-1-122-1-12-12-1-1-1-1-1-1-1-1-1-2-211-2-2111111111100002222000000-2-20000001111000000000000-1-1-1-1
χ222222222222222222-2-2-2-2-2-22-1222-1-1-122-1-12-12-1-1-1-1-1-1-1-1-1-2-211-2-211111111110000-2-2-2-200000022000000-1-1-1-10000000000001111
χ232222222222222222-2-2-2-2-2-2-12-1-1-1222-1-122-12-12-1-1-1-1-1-1-1-111-2-211-2-211111111222200000000-2-200001111000000000000-1-1-1-10000
χ242222222222222222-2-2-2-2-2-2-12-1-1-1222-1-122-12-12-1-1-1-1-1-1-1-111-2-211-2-211111111-2-2-2-200000000220000-1-1-1-100000000000011110000
χ25222-22-2-2-2222-2-2-22-22i−2i2i2i−2i−2i2-1222-1-1-1-2-211-21-21-1-1-1-111112i2i−i−i−2i−2iii−i−i−i−iiiii00002i2i−2i−2i0000002-2000000-1-111000000000000−i−iii
χ26222-22-2-2-2222-2-2-22-22i−2i2i2i−2i−2i2-1222-1-1-1-2-211-21-21-1-1-1-111112i2i−i−i−2i−2iii−i−i−i−iiiii0000−2i−2i2i2i000000-2200000011-1-1000000000000ii−i−i
χ27222-22-2-2-2222-2-2-22-22i−2i2i2i−2i−2i-12-1-1-122211-2-21-21-2-1-1-1-11111−i−i2i2iii−2i−2i−i−i−i−iiiii2i2i−2i−2i000000002-20000-1-111000000000000−i−iii0000
χ28222-22-2-2-2222-2-2-22-22i−2i2i2i−2i−2i-12-1-1-122211-2-21-21-2-1-1-1-11111−i−i2i2iii−2i−2i−i−i−i−iiiii−2i−2i2i2i00000000-22000011-1-1000000000000ii−i−i0000
χ29222-22-2-2-2222-2-2-22-2−2i2i−2i−2i2i2i2-1222-1-1-1-2-211-21-21-1-1-1-11111−2i−2iii2i2i−i−iiiii−i−i−i−i00002i2i−2i−2i000000-2200000011-1-1000000000000−i−iii
χ30222-22-2-2-2222-2-2-22-2−2i2i−2i−2i2i2i2-1222-1-1-1-2-211-21-21-1-1-1-11111−2i−2iii2i2i−i−iiiii−i−i−i−i0000−2i−2i2i2i0000002-2000000-1-111000000000000ii−i−i
χ31222-22-2-2-2222-2-2-22-2−2i2i−2i−2i2i2i-12-1-1-122211-2-21-21-2-1-1-1-11111ii−2i−2i−i−i2i2iiiii−i−i−i−i2i2i−2i−2i00000000-22000011-1-1000000000000−i−iii0000
χ32222-22-2-2-2222-2-2-22-2−2i2i−2i−2i2i2i-12-1-1-122211-2-21-21-2-1-1-1-11111ii−2i−2i−i−i2i2iiiii−i−i−i−i−2i−2i2i2i000000002-20000-1-111000000000000ii−i−i0000
χ3322-22-22-2-222-222-2-2-2000000222-2-22-2-2222-2-2-2-2222-2-222-2-200000000000000002i−2i2i−2i0000000000000000000000000000002i−2i2i−2i0000
χ3422-22-22-2-222-222-2-2-2000000222-2-22-2-2222-2-2-2-2222-2-222-2-20000000000000000−2i2i−2i2i000000000000000000000000000000−2i2i−2i2i0000
χ3522-22-22-2-222-222-2-2-2000000-12-1112-2-2-1-12-21-212-1-111-1-1113−3003−30033−3−333−3−32i−2i2i−2i00000000000000−i3i3−i3i3000000000000−ii−ii0000
χ3622-22-22-2-222-222-2-2-2000000-12-1112-2-2-1-12-21-212-1-111-1-1113−3003−30033−3−333−3−3−2i2i−2i2i00000000000000i3−i3i3−i3000000000000i−ii−i0000
χ3722-22-22-2-222-222-2-2-2000000-12-1112-2-2-1-12-21-212-1-111-1-111−3300−3300−3−333−3−3332i−2i2i−2i00000000000000i3−i3i3−i3000000000000−ii−ii0000
χ3822-22-22-2-222-222-2-2-2000000-12-1112-2-2-1-12-21-212-1-111-1-111−3300−3300−3−333−3−333−2i2i−2i2i00000000000000−i3i3−i3i3000000000000i−ii−i0000
χ3922-2-2-2-22222-2-2-22-22000000222-2-22-2-2-2-2-22222-222-2-2-2-22200000000000000002-2-220000000000000000000000000000002-2-220000
χ4022-2-2-2-22222-2-2-22-22000000222-2-22-2-2-2-2-22222-222-2-2-2-2220000000000000000-222-2000000000000000000000000000000-222-20000
χ4122-2-2-2-22222-2-2-22-22000000-12-1112-2-211-22-12-1-2-1-11111-1-1−i3i300i3−i300−i3−i3i3i3i3i3−i3−i32-2-2200000000000000−i3i3i3−i3000000000000-111-10000
χ4222-2-2-2-22222-2-2-22-22000000-12-1112-2-211-22-12-1-2-1-11111-1-1−i3i300i3−i300−i3−i3i3i3i3i3−i3−i3-222-200000000000000i3−i3−i3i30000000000001-1-110000
χ4322-2-2-2-22222-2-2-22-22000000-12-1112-2-211-22-12-1-2-1-11111-1-1i3−i300−i3i300i3i3−i3−i3−i3−i3i3i32-2-2200000000000000i3−i3−i3i3000000000000-111-10000
χ4422-2-2-2-22222-2-2-22-22000000-12-1112-2-211-22-12-1-2-1-11111-1-1i3−i300−i3i300i3i3−i3−i3−i3−i3i3i3-222-200000000000000−i3i3i3−i30000000000001-1-110000
χ452-222-2-22-22-222-22-2-200000022-22-2-22-22-222-2-22-22-22-22-22-2000000000000000000002i−2i2i−2i0000000000000000000000000000002i−2i2i−2i
χ462-222-2-22-22-222-22-2-200000022-22-2-22-22-222-2-22-22-22-22-22-200000000000000000000−2i2i−2i2i000000000000000000000000000000−2i2i−2i2i
χ472-222-2-22-22-222-22-2-20000002-1-22-21-112-2-1-1-2121-11-11-11-11003−3003−33−33−33−33−300002i−2i2i−2i00000000000000−i3i3−i3i3000000000000−ii−ii
χ482-222-2-22-22-222-22-2-20000002-1-22-21-112-2-1-1-2121-11-11-11-11003−3003−33−33−33−33−30000−2i2i−2i2i00000000000000i3−i3i3−i3000000000000i−ii−i
χ492-222-2-22-22-222-22-2-20000002-1-22-21-112-2-1-1-2121-11-11-11-1100−3300−33−33−33−33−3300002i−2i2i−2i00000000000000i3−i3i3−i3000000000000−ii−ii
χ502-222-2-22-22-222-22-2-20000002-1-22-21-112-2-1-1-2121-11-11-11-1100−3300−33−33−33−33−330000−2i2i−2i2i00000000000000−i3i3−i3i3000000000000i−ii−i
χ512-22-2-22-222-22-22-2-2200000022-22-2-22-2-22-2-222-222-22-2-22-22000000000000000000002-2-220000000000000000000000000000002-2-22
χ522-22-2-22-222-22-22-2-2200000022-22-2-22-2-22-2-222-222-22-2-22-2200000000000000000000-222-2000000000000000000000000000000-222-2
χ532-22-2-22-222-22-22-2-220000002-1-22-21-11-22112-1-2-1-11-111-11-100−i3i300i3−i3−i3i3−i3i3i3−i3i3−i300002-2-2200000000000000−i3i3i3−i3000000000000-111-1
χ542-22-2-22-222-22-22-2-220000002-1-22-21-11-22112-1-2-1-11-111-11-100−i3i300i3−i3−i3i3−i3i3i3−i3i3−i30000-222-200000000000000i3−i3−i3i30000000000001-1-11
χ552-22-2-22-222-22-22-2-220000002-1-22-21-11-22112-1-2-1-11-111-11-100i3−i300−i3i3i3−i3i3−i3−i3i3−i3i300002-2-2200000000000000i3−i3−i3i3000000000000-111-1
χ562-22-2-22-222-22-22-2-220000002-1-22-21-11-22112-1-2-1-11-111-11-100i3−i300−i3i3i3−i3i3−i3−i3i3−i3i30000-222-200000000000000−i3i3i3−i30000000000001-1-11
χ572-2-222-2-222-2-22-2-22200000022-2-22-2-222-22-222-2-22-2-222-2-220000000000000000000000002-22-2000000000000002-22-2000000000000
χ582-2-222-2-222-2-22-2-22200000022-2-22-2-222-22-222-2-22-2-222-2-22000000000000000000000000-22-2200000000000000-22-22000000000000
χ592-2-2-2222-22-2-2-2222-200000022-2-22-2-22-22-22-2-2222-2-22-222-20000000000000000000000002-2-22000000000000002-2-22000000000000
χ602-2-2-2222-22-2-2-2222-200000022-2-22-2-22-22-22-2-2222-2-22-222-2000000000000000000000000-222-200000000000000-222-2000000000000
χ614444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-211111111-2-2-2-2-2-2-2-211111111000000000000000000000000000000000000000000
χ624444444444444444-4-4-4-4-4-4-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21111111122222222-1-1-1-1-1-1-1-1000000000000000000000000000000000000000000
χ63444-44-4-4-4444-4-4-44-44i−4i4i4i−4i−4i-2-2-2-2-2-2-2-2222222221111-1-1-1-1−2i−2i−2i−2i2i2i2i2iiiii−i−i−i−i000000000000000000000000000000000000000000
χ64444-44-4-4-4444-4-4-44-4−4i4i−4i−4i4i4i-2-2-2-2-2-2-2-2222222221111-1-1-1-12i2i2i2i−2i−2i−2i−2i−i−i−i−iiiii000000000000000000000000000000000000000000
χ6544-44-44-4-444-444-4-4-40000004-24-4-4-22244-22-42-4-2-2-222-2-2220000000000000000000000000000000000000000000000000000000000
χ6644-44-44-4-444-444-4-4-4000000-2-2-222-222-2-2-22222-211-1-111-1-123−230023−2300−3−333−3−333000000000000000000000000000000000000000000
χ6744-44-44-4-444-444-4-4-4000000-2-2-222-222-2-2-22222-211-1-111-1-1−232300−23230033−3−333−3−3000000000000000000000000000000000000000000
χ6844-4-4-4-44444-4-4-44-440000004-24-4-4-222-4-42-24-242-2-22222-2-20000000000000000000000000000000000000000000000000000000000
χ6944-4-4-4-44444-4-4-44-44000000-2-2-222-222222-2-2-2-2211-1-1-1-111−2i32i3002i3−2i300i3i3−i3−i3−i3−i3i3i3000000000000000000000000000000000000000000
χ7044-4-4-4-44444-4-4-44-44000000-2-2-222-222222-2-2-2-2211-1-1-1-1112i3−2i300−2i32i300−i3−i3i3i3i3i3−i3−i3000000000000000000000000000000000000000000
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χ734-444-4-44-44-444-44-4-4000000-2-22-222-22-22-2-222-221-11-11-11-100−232300−23233−33−33−33−3000000000000000000000000000000000000000000
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χ754-44-4-44-444-44-44-4-44000000-2-22-222-222-222-2-22-21-11-1-11-1100−2i32i3002i3−2i3i3−i3i3−i3−i3i3−i3i3000000000000000000000000000000000000000000
χ764-44-4-44-444-44-44-4-44000000-2-22-222-222-222-2-22-21-11-1-11-11002i3−2i300−2i32i3−i3i3−i3i3i3−i3i3−i3000000000000000000000000000000000000000000
χ774-4-444-4-444-4-44-4-4440000004-2-4-4422-24-4-224-2-42-222-2-222-20000000000000000000000000000000000000000000000000000000000
χ784-4-444-4-444-4-44-4-444000000-2422-2-4-44-224-4-242-4-222-2-222-20000000000000000000000000000000000000000000000000000000000
χ794-4-444-4-444-4-44-4-444000000-2-222-222-2-22-22-2-2221-1-111-1-11000000003-3-333-3-33000000000000000000000000000000000000000000
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χ814-4-4-4444-44-4-4-4444-40000004-2-4-4422-2-442-2-424-2-222-22-2-220000000000000000000000000000000000000000000000000000000000
χ824-4-4-4444-44-4-4-4444-4000000-2422-2-4-442-2-442-4-24-222-22-2-220000000000000000000000000000000000000000000000000000000000
χ834-4-4-4444-44-4-4-4444-4000000-2-222-222-22-22-222-2-21-1-11-111-1000000003i−3i−3i3i−3i3i3i−3i000000000000000000000000000000000000000000
χ844-4-4-4444-44-4-4-4444-4000000-2-222-222-22-22-222-2-21-1-11-111-100000000−3i3i3i−3i3i−3i−3i3i000000000000000000000000000000000000000000
χ8566666666-3-3-3-3-3-3-3-366-3-3-3-3000000000000000000000000000000000000000000000000222200002200000000-1-1-1-1-1-1-1-100000000
χ8666666666-3-3-3-3-3-3-3-366-3-3-3-3000000000000000000000000000000000000000000000000-2-2-2-20000-2-2000000001111111100000000
χ8766666666-3-3-3-3-3-3-3-3-6-6333300000000000000000000000000000000000000000000000022220000-2-200000000-1-1-1-1111100000000
χ8866666666-3-3-3-3-3-3-3-3-6-63333000000000000000000000000000000000000000000000000-2-2-2-2000022000000001111-1-1-1-100000000
χ89666-66-6-6-6-3-3-3333-336i−6i−3i−3i3i3i00000000000000000000000000000000000000000000000022-2-200002i−2i00000000-1-111−i−iii00000000
χ90666-66-6-6-6-3-3-3333-336i−6i−3i−3i3i3i000000000000000000000000000000000000000000000000-2-2220000−2i2i0000000011-1-1ii−i−i00000000
χ91666-66-6-6-6-3-3-3333-33−6i6i3i3i−3i−3i00000000000000000000000000000000000000000000000022-2-20000−2i2i00000000-1-111ii−i−i00000000
χ92666-66-6-6-6-3-3-3333-33−6i6i3i3i−3i−3i000000000000000000000000000000000000000000000000-2-22200002i−2i0000000011-1-1−i−iii00000000
χ936-6-666-6-66-333-333-3-300−3i33i3−3i33i30000000000000000000000000000000000000000000000002-22-200000000000000-11-11−i3i3−i3i300000000
χ946-6-666-6-66-333-333-3-300−3i33i3−3i33i3000000000000000000000000000000000000000000000000-22-22000000000000001-11-1i3−i3i3−i300000000
χ956-6-666-6-66-333-333-3-3003i3−3i33i3−3i30000000000000000000000000000000000000000000000002-22-200000000000000-11-11i3−i3i3−i300000000
χ966-6-666-6-66-333-333-3-3003i3−3i33i3−3i3000000000000000000000000000000000000000000000000-22-22000000000000001-11-1−i3i3−i3i300000000
χ976-6-6-6666-6-3333-3-3-330033−33−33330000000000000000000000000000000000000000000000002-2-2200000000000000-111-13−3−3300000000
χ986-6-6-6666-6-3333-3-3-330033−33−3333000000000000000000000000000000000000000000000000-222-2000000000000001-1-11−333−300000000
χ996-6-6-6666-6-3333-3-3-3300−333333−330000000000000000000000000000000000000000000000002-2-2200000000000000-111-1−333−300000000
χ1006-6-6-6666-6-3333-3-3-3300−333333−33000000000000000000000000000000000000000000000000-222-2000000000000001-1-113−3−3300000000
χ1011212-1212-1212-12-12-6-66-6-66660000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1021212-12-12-12-121212-6-6666-66-60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10312-121212-12-1212-12-66-6-66-6660000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10412-1212-12-1212-1212-66-66-666-60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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