Finite Group Databasebeta

← Group #13168629

Character table — Group #13168629

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size11112222222222222244444444444444444488888888888888999912121212121212121212121212121818181818181818181818181818242424242424242424242424242424242424242436363636363636363636108108
order1222333446666666663336666666661212121212123666121212121212121212124444224444666612121212224444444412121212666666121212121212121212121212121266121212121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-11111111111-1-1-1-1-1-111-1-1111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-111
χ4111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ511111111111111111111111111111111111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111
χ711111111111111111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-111-1-1
χ811111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ91111111-1-1111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111-11-11-111-1-111-1-111-1-111-1-1-1-111111-111-1-11-11-11-111-1-111-1-111-1-111-1-1-1-11-1
χ101111111-1-1111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111-1-111-111-1-111-1-1-1-111-1-1-1-11111111-111-1-11-1-11-1111-1-1-1-111-1-1-1-1-1-11111-11
χ111111111-1-1111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-111-1-11-1-111-1-111-1-111-1-1-1-1111111-11-1-111-111-11-1-1-11111-1-1-1-1-1-1-1-111111-1
χ121111111-1-1111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-11-11-11-1-111-1-11111-1-111-1-1-1-11111-11-1-111-11-11-11-1-111-1-11111-1-111-1-1-1-1-11
χ131111111-1-1111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1111-1-1-1-111-1-1111111-1-1-1-1-1-11-111-1-1-111-11-1-1-11111-1-1-1-11111-1-111-11
χ141111111-1-1111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1111-1-1-1-11111-1-1-1-11111-1-1-1-11-111-1-1-11-11-11-1-111-1-1111111-1-111-1-11-1
χ151111111-1-1111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-11111-1-111-1-1-1-11111-1-1-1-1-11-1-1111-11-11-111-1-111-1-11111-1-111-1-1-11
χ161111111-1-1111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-11-1-1111-1-11-1111-1-1-1-111-1-11111-1-1111-1
χ17222222-122-12-122222-1-1-12-1-1-122-12-1-12222-1-1-1-1-1-122-1-1-1-1-1-1-1-100000022220000222222220000000000000000-1-122-1-1-1-1-1-1-1-1-1-1-1-1000000-1-100
χ18222222-122-12-122222-1-1-12-1-1-122-12-1-12222-1-1-1-1-1-122-1-1-1-1-1-1-1-100000022-2-20000-2-2-2-2-2-2-2-200000000000000001122-1-11111-1-1-1-1110000001100
χ19222222-122-12-122222-1-1-12-1-1-122-12-1-12222-1-1-1-1-1-122-1-1-1-1-1-1-1-1000000-2-22200002222-2-2-2-20000000000000000-1-1-2-211-1-1-1-11111110000001100
χ20222222-122-12-122222-1-1-12-1-1-122-12-1-12222-1-1-1-1-1-122-1-1-1-1-1-1-1-1000000-2-2-2-20000-2-2-2-22222000000000000000011-2-21111111111-1-1000000-1-100
χ21222222-1-2-2-12-122222-1-1-12-1-1-122-12-1-1-2-2-2-211-1-1-1-1-2-2111111110000002-22-2000022-2-222-2-20000000000000000-112-2-11-1-111-1-111-1-10000001100
χ22222222-1-2-2-12-122222-1-1-12-1-1-122-12-1-1-2-2-2-211-1-1-1-1-2-2111111110000002-2-220000-2-222-2-22200000000000000001-12-2-1111-1-1-1-11111000000-1-100
χ23222222-1-2-2-12-122222-1-1-12-1-1-122-12-1-1-2-2-2-211-1-1-1-1-2-211111111000000-222-2000022-2-2-2-2220000000000000000-11-221-1-1-11111-1-111000000-1-100
χ24222222-1-2-2-12-122222-1-1-12-1-1-122-12-1-1-2-2-2-211-1-1-1-1-2-211111111000000-22-220000-2-22222-2-200000000000000001-1-221-111-1-111-1-1-1-10000001100
χ2522222-1222222-12-1-1222-1-12-1-1-1-12-12-122-1-122-1-1-1-1-1-122-1-1-1-1-1-100002222002222000000002200220000-1-1-1-1-1-100-1-1220000-1-1-1-10000-1-1-1-10000
χ2622222-1222222-12-1-1222-1-12-1-1-1-12-12-122-1-122-1-1-1-1-1-122-1-1-1-1-1-1000022-2-200222200000000-2-200-2-20000-1-1-1-1-1-10011-2-200001111000011110000
χ2722222-1222222-12-1-1222-1-12-1-1-1-12-12-122-1-122-1-1-1-1-1-122-1-1-1-1-1-10000-2-22200-2-2-2-200000000-2-200-2-2000011111100-1-1220000-1-1-1-1000011110000
χ2822222-1222222-12-1-1222-1-12-1-1-1-12-12-122-1-122-1-1-1-1-1-122-1-1-1-1-1-10000-2-2-2-200-2-2-2-20000000022002200001111110011-2-2000011110000-1-1-1-10000
χ2922222-12-2-2222-12-1-1222-1-12-1-1-1-12-12-1-2-211-2-2-1-1-1-111-2-211111100002-22-20022-2-2000000002200-2-20000-11-1-11100-112-20000-1-1110000-1-1110000
χ3022222-12-2-2222-12-1-1222-1-12-1-1-1-12-12-1-2-211-2-2-1-1-1-111-2-211111100002-2-220022-2-200000000-2-200220000-11-1-111001-1-22000011-1-1000011-1-10000
χ3122222-12-2-2222-12-1-1222-1-12-1-1-1-12-12-1-2-211-2-2-1-1-1-111-2-21111110000-222-200-2-22200000000-2-2002200001-111-1-100-112-20000-1-111000011-1-10000
χ3222222-12-2-2222-12-1-1222-1-12-1-1-1-12-12-1-2-211-2-2-1-1-1-111-2-21111110000-22-2200-2-222000000002200-2-200001-111-1-1001-1-22000011-1-10000-1-1110000
χ332222-122222-122-122-12-12-1-122-1-1-1-1-12-1-12222-1-1-1-1-1-1-1-122-1-1-1-12222220022-1-1-1-1-1-1-1-10000002200-1-1-1-122-1-1-1-1220000-1-1-1-1000000-1-100000000
χ342222-122222-122-122-12-12-1-122-1-1-1-1-12-1-12222-1-1-1-1-1-1-1-122-1-1-1-12222-2-200-2-2111111110000002200-1-1-1-1-2-21111-2-200001111000000-1-100000000
χ352222-122222-122-122-12-12-1-122-1-1-1-1-12-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-22200-2-2-1-1-1-11111000000-2-200111122-1-1-1-1-2-2000011110000001100000000
χ362222-122222-122-122-12-12-1-122-1-1-1-1-12-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-2-2-200221111-1-1-1-1000000-2-2001111-2-21111220000-1-1-1-10000001100000000
χ372222-122-2-22-122-122-12-12-1-122-1-1-1-1-1211-2-2-2-2-1-1-1-11111-2-2111122222-2002-2-1-111-1-111000000-2-200-1-1-1-12-2-1-1112-20000-1-1110000001100000000
χ382222-122-2-22-122-122-12-12-1-122-1-1-1-1-1211-2-2-2-2-1-1-1-11111-2-211112222-2200-2211-1-111-1-1000000-2-200-1-1-1-1-2211-1-1-22000011-1-10000001100000000
χ392222-122-2-22-122-122-12-12-1-122-1-1-1-1-1211-2-2-2-2-1-1-1-11111-2-21111-2-2-2-22-200-22-1-11111-1-1000000220011112-2-1-111-22000011-1-1000000-1-100000000
χ402222-122-2-22-122-122-12-12-1-122-1-1-1-1-1211-2-2-2-2-1-1-1-11111-2-21111-2-2-2-2-22002-211-1-1-1-11100000022001111-2211-1-12-20000-1-111000000-1-100000000
χ4122-2-22222-2-22-22-2-2-2-22222-2-2-2-2-222-222-22-22-22-2-222-22-22-222-2-22i2i−2i−2i000000000000000000002i−2i002i2i−2i−2i00000000000000000000002i−2i00000000
χ4222-2-22222-2-22-22-2-2-2-22222-2-2-2-2-222-222-22-22-22-2-222-22-22-222-2-2−2i−2i2i2i00000000000000000000−2i2i00−2i−2i2i2i0000000000000000000000−2i2i00000000
χ4322-2-2222-22-22-22-2-2-2-22222-2-2-2-2-222-22-22-22-222-2-22-22-22-22-2-2222i2i−2i−2i00000000000000000000−2i2i002i2i−2i−2i0000000000000000000000−2i2i00000000
χ4422-2-2222-22-22-22-2-2-2-22222-2-2-2-2-222-22-22-22-222-2-22-22-22-22-2-222−2i−2i2i2i000000000000000000002i−2i00−2i−2i2i2i00000000000000000000002i−2i00000000
χ4522-2-2-1222-2-2-1-221-2-212-12-11-2-211-1-112-112-22-2-111-1-11-112-2-1-1112i2i−2i−2i000000−i3i3−i3i33−33−30000002i−2i00−i−iii00−i3i3−i3i30000003−33−3000000−ii00000000
χ4622-2-2-1222-2-2-1-221-2-212-12-11-2-211-1-112-112-22-2-111-1-11-112-2-1-1112i2i−2i−2i000000i3−i3i3−i3−33−330000002i−2i00−i−iii00i3−i3i3−i3000000−33−33000000−ii00000000
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χ4822-2-2-1222-2-2-1-221-2-212-12-11-2-211-1-112-112-22-2-111-1-11-112-2-1-111−2i−2i2i2i000000i3−i3i3−i33−33−3000000−2i2i00ii−i−i00i3−i3i3−i30000003−33−3000000i−i00000000
χ4922-2-2-122-22-2-1-221-2-212-12-11-2-211-1-1121-1-22-22-111-11-11-1-2211-1-12i2i−2i−2i000000−i3i3i3−i33−3−33000000−2i2i00−i−iii00−i3i3i3−i30000003−3−33000000i−i00000000
χ5022-2-2-122-22-2-1-221-2-212-12-11-2-211-1-1121-1-22-22-111-11-11-1-2211-1-12i2i−2i−2i000000i3−i3−i3i3−333−3000000−2i2i00−i−iii00i3−i3−i3i3000000−333−3000000i−i00000000
χ5122-2-2-122-22-2-1-221-2-212-12-11-2-211-1-1121-1-22-22-111-11-11-1-2211-1-1−2i−2i2i2i000000−i3i3i3−i3−333−30000002i−2i00ii−i−i00−i3i3i3−i3000000−333−3000000−ii00000000
χ5222-2-2-122-22-2-1-221-2-212-12-11-2-211-1-1121-1-22-22-111-11-11-1-2211-1-1−2i−2i2i2i000000i3−i3−i3i33−3−330000002i−2i00ii−i−i00i3−i3−i3i30000003−3−33000000−ii00000000
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χ572-2-22222002-2-2-22-22-2-22222-22-22-2-2-2-20000002-22-200000000002i−2i−2i2i000000000000002-2002i−2i00002i−2i−2i2i000000000000000000002-2002i−2i000000
χ582-2-22222002-2-2-22-22-2-22222-22-22-2-2-2-20000002-22-200000000002i−2i−2i2i00000000000000-2200−2i2i00002i−2i−2i2i00000000000000000000-2200−2i2i000000
χ592-2-22222002-2-2-22-22-2-22222-22-22-2-2-2-20000002-22-20000000000−2i2i2i−2i000000000000002-200−2i2i0000−2i2i2i−2i000000000000000000002-200−2i2i000000
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χ6144444-2-244-24-2-24-2-24-2-21-2-211-2-2-2-2-2144-2-2-2-21111-2-2-2-21111110000004400000000000000000000000000000000-2-2-2-200001111000000000000
χ6244444-2-244-24-2-24-2-24-2-21-2-211-2-2-2-2-2144-2-2-2-21111-2-2-2-2111111000000-4-40000000000000000000000000000000022220000-1-1-1-1000000000000
χ6344444-2-2-4-4-24-2-24-2-24-2-21-2-211-2-2-2-2-21-4-4222211112222-1-1-1-1-1-10000004-400000000000000000000000000000000-22-22000011-1-1000000000000
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χ8544-4-4-2-244-4-4-2-4-222224-2-21222-1-1-212-2-22-224-41-1-111-1-22-2211-1-10000000000−2i32i3−2i32i300000000000000000000i3−i3i3−i300000000000000000000000000
χ8644-4-4-2-244-4-4-2-4-222224-2-21222-1-1-212-2-22-224-41-1-111-1-22-2211-1-100000000002i3−2i32i3−2i300000000000000000000−i3i3−i3i300000000000000000000000000
χ8744-4-4-2-24-44-4-2-4-222224-2-21222-1-1-212-22-22-2-441-1-11-112-22-2-1-1110000000000−2i32i32i3−2i300000000000000000000i3−i3−i3i300000000000000000000000000
χ8844-4-4-2-24-44-4-2-4-222224-2-21222-1-1-212-22-22-2-441-1-11-112-22-2-1-11100000000002i3−2i3−2i32i300000000000000000000−i3i3i3−i300000000000000000000000000
χ894-44-444-2002-4-2-4-44-442-2-242-224-42-4-22000000-2-2220000000000000000000000000000004i−4i00000000000000000000000000000000000000−2i2i00
χ904-44-444-2002-4-2-4-44-442-2-242-224-42-4-22000000-2-222000000000000000000000000000000−4i4i000000000000000000000000000000000000002i−2i00
χ914-44-44-2400-4-442-4-224-44-2-2-4-22-22-4242000000-2-2220000000000000000000000000000000000004i−4i000000000000000000000000000000−2i2i0000
χ924-44-44-2400-4-442-4-224-44-2-2-4-22-22-4242000000-2-222000000000000000000000000000000000000−4i4i0000000000000000000000000000002i−2i0000
χ934-44-4-24400-424-424-4-2-4-24-224-4-2222-2-4000000-2-22200000000004-44-4000000000000000000000000-22-2200000000000000000000000000000000
χ944-44-4-24400-424-424-4-2-4-24-224-4-2222-2-4000000-2-2220000000000-44-440000000000000000000000002-22-200000000000000000000000000000000
χ954-4-4444-200-2-42-44-44-42-2-24-22-2-442-422000000-22-2200000000000000000000000000004-400000000000000000000000000000000-220000000000
χ964-4-4444-200-2-42-44-44-42-2-24-22-2-442-422000000-22-220000000000000000000000000000-44000000000000000000000000000000002-20000000000
χ974-4-444-24004-4-4242-2-4-44-2-242-22-2-42-42000000-22-22000000000000000000000000000000004i−4i00000000000000000000000000000000−2i2i000000
χ984-4-444-24004-4-4242-2-4-44-2-242-22-2-42-42000000-22-2200000000000000000000000000000000−4i4i000000000000000000000000000000002i−2i000000
χ994-4-44-2440042-4-4-2-442-4-24-2-2-442-2222-4000000-22-2200000000004i−4i−4i4i000000000000000000000000−2i2i2i−2i00000000000000000000000000000000
χ1004-4-44-2440042-4-4-2-442-4-24-2-2-442-2222-4000000-22-220000000000−4i4i4i−4i0000000000000000000000002i−2i−2i2i00000000000000000000000000000000
χ1018888-4-4-488-4-4-4-4-4-4-4-4-4222222222222-4-4-4-4-4-4-1-1-1-1222222-1-1-1-10000000000000000000000000000000000000000000000000000000000000000
χ1028888-4-4-4-8-8-4-4-4-4-4-4-4-4-4222222222222444444-1-1-1-1-2-2-2-2-2-211110000000000000000000000000000000000000000000000000000000000000000
χ10388-8-8-4-4-48-84-44-44444-4222-2-2-2-2-222-22-44-44-44-111-12-22-22-2-1-1110000000000000000000000000000000000000000000000000000000000000000
χ10488-8-8-4-4-4-884-44-44444-4222-2-2-2-2-222-224-44-44-4-111-1-22-22-2211-1-10000000000000000000000000000000000000000000000000000000000000000
χ1058-88-88-4-4004-8-44-8-4484-42-442-2-4444-4-200000022-2-200000000000000000000000000000000000000000000000000000000000000000000000000
χ1068-88-8-48-40044-4-848-8-442-4-4-2-44-44-242400000022-2-200000000000000000000000000000000000000000000000000000000000000000000000000
χ1078-88-8-4-4800-84844-44-4-8-4-424-442-24-2-4400000022-2-200000000000000000000000000000000000000000000000000000000000000000000000000
χ1088-88-8-4-4-40044-444-44-44222-22-22-2-2-22-2000000-1-11100000033−3333−330000000000000000000000000000000000000000000000000000000000000000
χ1098-88-8-4-4-40044-444-44-44222-22-22-2-2-22-2000000-1-111000000−3333−33330000000000000000000000000000000000000000000000000000000000000000
χ1108-8-888-4-400-4-84484-4-84-42-4-4-224-4444-20000002-22-200000000000000000000000000000000000000000000000000000000000000000000000000
χ1118-8-88-48-400-444-8-4-88442-4-424-44-4-24-240000002-22-200000000000000000000000000000000000000000000000000000000000000000000000000
χ1128-8-88-4-480084-84-44-44-8-4-42-44-4-224-2440000002-22-200000000000000000000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4-4-400-4444-44-4442222-22-22-2-2-2-2000000-11-1100000033−33−33330000000000000000000000000000000000000000000000000000000000000000
χ1148-8-88-4-4-400-4444-44-4442222-22-22-2-2-2-2000000-11-11000000−333333−330000000000000000000000000000000000000000000000000000000000000000

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