Finite Group Databasebeta

← Group #13168591

Character table — Group #13168591

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size111122222222222244444444444444444444466888888888888812121212121212121212121212121212121212121212121212181824242424242424242424242424243636363636363654547272727272108
order122233366666666633346666666661212121212121212443666121212121212121212224446666666666121212121212121212124466612121212121212121212124444412124412121212122
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1111111111111-1-1111111-1-11111-1-11-111-1-1-1-111-1-1-1-1-1-1-11-11-1-1-1
χ311111111111111111111111111111111111111111111111111111-1-11111-1-11111111111111111-1-1-1-1-1-111-11-1-11111-1-111-1-1-1-1-1-1-1-111-1
χ411111111111111111111111111111111111111111111111111111-1-1-1-111-1-111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11-1-1-11
χ51111111111111111111111111111111111111-1-11111111111111-11111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111111111-1-1-1-1111-1-1-11-1-1-1-1
χ61111111111111111111111111111111111111-1-11111111111111-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-111-1-1-1-1-1-111-1-1-111-1-1-1111
χ71111111111111111111111111111111111111-1-11111111111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1111111-1-1-1-1-1111-11-1-11
χ81111111111111111111111111111111111111-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-111111-1
χ91111111111111111111-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-11-1-1-111-1-1-1-1-1-1111111111111111-11-1-1-1-1-111-1-11-11-1-111111-1-11-1-1
χ101111111111111111111-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-1-11-1-111-1-1-1-1-1-111-1-1111111-1-1111-1-11-11-1-1-1-1111-1-111-1-1-1-111-1-111
χ111111111111111111111-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-111-11-11111-1-1-111-11-1-1-1-1-1111-11
χ121111111111111111111-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-11-111111-1-111-11-11-11111-1-11-11-1
χ131111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-11-11111111111-1-111-1-1-1-1-1-111111-11-1-1-1-1-111-1-1-11-11-111-1-1-1-11-111
χ141111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-11-1-1-1-111-111-11-1-111-1111-1-1
χ151111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-111-111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-111-11-11111-1-11-1-111-1-11111-1-11-1
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-11-1111-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-11-111111-1-1111-11-1-111-1-11-1-11-11
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χ18222222-122-12-12-1222-1-122-1-1-12-1-1-12-1-122-1-1-1-122-1-1-1-1222-1-1-1-1-1-12-2-20022-2-2-1-1-1-1-1-1-1-10022-1-1-1-100111100-20110000-2-20000000101000
χ19222222-122-12-12-1222-1-122-1-1-12-1-1-12-1-122-1-1-1-1-2-2-1-1-1-1222-1-1-1-1-1-1-22200-2-2221111111100-2-2111100-1-1-1-10020-1-10000-2-20000000101000
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χ23222222-122-12-12-1222-1-1-22-1-1-12-1-1-1211-2-21111-2-2-1-1-1-1-2-2-211111122-2002222-1-1-1-1-1-11100-2-2111100-1-1-1100-20110000-22000000010-1000
χ24222222-122-12-12-1222-1-1-22-1-1-12-1-1-1211-2-21111-2-2-1-1-1-1-2-2-21111112-220022-2-2-1-1-1-1-1-11100-2-2111100111-10020-1-100002-20000000-101000
χ2522222-122-1222-12-12-12-12-122-1-1-1-12-12222222200-1-1-1-1-1-1-1-1-1-1-1-1-10222200-1-100000000-1-1000000222-1-1222-1-1-1-1-1-1-1-100002-1-1000-10000
χ2622222-122-1222-12-12-12-12-122-1-1-1-12-12222222200-1-1-1-1-1-1-1-1-1-1-1-1-1022-2-200-1-10000000011000000-2-22-1-12-2-2-11-1-111110000-21100010000
χ2722222-122-1222-12-12-12-12-122-1-1-1-12-12222222200-1-1-1-1-1-1-1-1-1-1-1-1-10-2-222001100000000-1-1000000-2-2-211-2221-111-1-1-1-10000-21100010000
χ2822222-122-1222-12-12-12-12-122-1-1-1-12-12222222200-1-1-1-1-1-1-1-1-1-1-1-1-10-2-2-2-20011000000001100000022-211-2-2-21111111100002-1-1000-10000
χ2922222-122-1222-12-12-12-1-2-122-1-1-1-12-1-2-2-2-2-2-2-2-200-1-1-1-111111111102-22-200-1-100000000-1-1000000222-1-1-22-21111-1-1110000-2-1-100010000
χ3022222-122-1222-12-12-12-1-2-122-1-1-1-12-1-2-2-2-2-2-2-2-200-1-1-1-111111111102-2-2200-1-10000000011000000-2-22-1-1-2-221-11111-1-10000211000-10000
χ3122222-122-1222-12-12-12-1-2-122-1-1-1-12-1-2-2-2-2-2-2-2-200-1-1-1-11111111110-222-2001100000000-1-1000000-2-2-21122-2-11-1-1-1-1110000211000-10000
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χ342222-122-122-12222-1-1-122-1-1-12-122-1-122-1-1-1-1-1-122-1-1-1-12-1-122-1-1-1-1200-2-2-1-10022-1-1-1-122-2-2-1-1-1-1-1-1000000110-200111100-2-200000000110
χ352222-122-122-12222-1-1-122-1-1-12-122-1-122-1-1-1-1-1-1-2-2-1-1-1-12-1-122-1-1-1-1-200221100-2-21111-2-222111111000000-1-10200-1-1-1-100-2-200000000110
χ362222-122-122-12222-1-1-122-1-1-12-122-1-122-1-1-1-1-1-1-2-2-1-1-1-12-1-122-1-1-1-1-200-2-21100-2-21111-2-2-2-2111111000000110-2001111002200000000-1-10
χ372222-122-122-12222-1-1-12-2-1-1-12-122-1-1-2-211111122-1-1-1-1-211-2-21111-2002-21100-2-211112222-1-1-1-1-1-1000000-110-200-1-111002-200000000-110
χ382222-122-122-12222-1-1-12-2-1-1-12-122-1-1-2-211111122-1-1-1-1-211-2-21111-200-221100-2-2111122-2-2-1-1-1-1-1-10000001-1020011-1-100-22000000001-10
χ392222-122-122-12222-1-1-12-2-1-1-12-122-1-1-2-2111111-2-2-1-1-1-1-211-2-211112002-2-1-10022-1-1-1-1-2-222111111000000-110-200-1-11100-22000000001-10
χ402222-122-122-12222-1-1-12-2-1-1-12-122-1-1-2-2111111-2-2-1-1-1-1-211-2-21111200-22-1-10022-1-1-1-1-2-2-2-21111110000001-1020011-1-1002-200000000-110
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χ914-4-44-24-22-42224-2-4-2-21-202-1-12-2-2212002i3−2i3−i3i3i3−i3001-1-1102i3−2i300−i3i3i3−i3000000000−2i32i3i3−i3−i3i3000000-333-30000000000000000000000000000000
χ924-4-44-24-22-42224-2-4-2-21-202-1-12-2-2212002i3−2i3−i3i3i3−i3001-1-1102i3−2i300−i3i3i3−i30000000002i3−2i3−i3i3i3−i30000003-3-330000000000000000000000000000000
χ934-4-44-2-2422-42-4-242-21-2-20-12221-22-2-100−2i32i3−2i32i32i3−2i3001-1-110i3−i300i3−i3−i3i30000000000000000023−23000000000000000000−333i−3i000000000000000
χ944-4-44-2-2422-42-4-242-21-2-20-12221-22-2-100−2i32i3−2i32i32i3−2i3001-1-110i3−i300i3−i3−i3i300000000000000000−23230000000000000000003−3−3i3i000000000000000
χ954-4-44-2-2422-42-4-242-21-2-20-12221-22-2-1002i3−2i32i3−2i3−2i32i3001-1-110−i3i300−i3i3i3−i30000000000000000023−23000000000000000000−33−3i3i000000000000000
χ964-4-44-2-2422-42-4-242-21-2-20-12221-22-2-1002i3−2i32i3−2i3−2i32i3001-1-110−i3i300−i3i3i3−i300000000000000000−23230000000000000000003−33i−3i000000000000000
χ978888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-4-4-4222200-1-1-1-1-42222-1-1-1-100000000000000000000000000000000000000000000000000000000
χ988888-4-4-4-4-4-4-4-4-4-4-4-4222-82222222224444-2-2-2-200-1-1-1-14-2-2-2-2111100000000000000000000000000000000000000000000000000000000
χ9988-8-88-4-4-84-48444-4-8-4-4204-44-24-224-4000000000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ10088-8-8-4-48448-4-84-8-442-4-40-2-444-24-442000000000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-4-444-4-4444-442220-22-2-2-2-22-2200006i6i−6i−6i00-1-11100000−3i−3i3i3i00000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-4-444-4-4444-442220-22-2-2-2-22-220000−6i−6i6i6i00-1-111000003i3i−3i−3i00000000000000000000000000000000000000000000000000000000
χ1038-88-8-4-48-4-4-8484-8442-4-4024-4-4-2444-200000000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1048-88-8-4-4-4-4-444-4444422202-222-2-2-2-2-243−4300−2323−232300-11-11000−23233−33−300000000000000000000000000000000000000000000000000000000
χ1058-88-8-4-4-4-4-444-4444422202-222-2-2-2-2-2−43430023−2323−2300-11-1100023−23−33−3300000000000000000000000000000000000000000000000000000000
χ1068-8-888-4-4-844-84-4-448-4-420444-2-42-2-4400000000002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-444444-4-44-42220-2-2-2-222-22-200−4i34i32i3−2i3−2i32i300-111-102i3−2i300−i3i3i3−i300000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-444444-4-44-42220-2-2-2-222-22-2004i3−4i3−2i32i32i3−2i300-111-10−2i32i300i3−i3−i3i300000000000000000000000000000000000000000000000000000000

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