Finite Group Databasebeta

← Group #13168104

Character table — Group #13168104

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size111122222222222244444444444444444444466888888888888812121212121212121212121212121212121212121212121212181824242424242424242424242424243636363636363654547272727272108
order1222333666666666333466666666612121212121212124436661212121212121212122222466666666666612121212121212122266666666661212121244444664412121212124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1111111-1-1111111111111-1-1-1111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1
χ311111111111111111111111111111111111111111111111111111-1-1111111-1-111111111111111-1-11-1-1-111-1-1-1-11111-1-11-11-1-1-1-11-11-1-1-1
χ411111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-11-1-1-11
χ51111111111111111111111111111111111111-1-11111111111111-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-11-111-1-1-11-1-1-1-1
χ61111111111111111111111111111111111111-1-11111111111111-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11111-1-1-1-1-1-11-11-1-1111-11-1-11
χ71111111111111111111111111111111111111-1-11111111111111-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111-1-1-1-1111111-1-1-1-1-111-1-1-1111
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
χ91111111111111111111-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-11111-1-1-1-1111111111111-1-11111-1-1-1-1-1-11-11-1-111111-1-11-1-1
χ101111111111111111111-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-111-1-1-1-1-1-111111111-1-1-11-1-1-1-111-1-111111-1-111-1-1-1-1-1111-11
χ111111111111111111111-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111-1-1-1-111111111-1-11-11111-1-111-1-1-1-1-1111-1-1-1-1-111-1-111
χ121111111111111111111-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1111111-11-1-111111-1-11-11-1
χ131111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-11-1111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-11-1-1111-1-1-1-11-111
χ141111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-11111111-1-11111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111-1-11111-1111-1-1-11111-1-11-1
χ151111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-111-11111-1-1111111-1-1-1-1-1-1-1-1-1-11-11111-1-111-1-1-1-11-1-111-1-111-1111-1-1
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-11-111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111111-11-1-111-1-11-1-11-11
χ17222222-12-12-122-1222-1-1222-1-1-1-1-1-122222222200-1-1-1-1-1-1-1-1-1-1-1-1-1022220000-1-1-1-100000000000022222-1-1-1-1-1-1-12-1-1-100020-1-1000-10000
χ18222222-12-12-122-1222-1-1222-1-1-1-1-1-122222222200-1-1-1-1-1-1-1-1-1-1-1-1-1022-2-20000-1-111000000000000-2-2-222-111-1-1-1-1-2111000-201100010000
χ19222222-12-12-122-1222-1-1222-1-1-1-1-1-122222222200-1-1-1-1-1-1-1-1-1-1-1-1-10-2-222000011-1-1000000000000-2-22-2-21-1-111112-1-1-1000-201100010000
χ20222222-12-12-122-1222-1-1222-1-1-1-1-1-122222222200-1-1-1-1-1-1-1-1-1-1-1-1-10-2-2-2-20000111100000000000022-2-2-21111111-211100020-1-1000-10000
χ21222222-12-12-122-1222-1-1-222-1-1-1-1-1-12-2-2-2-2-2-2-2-200-1-1-1-111111111102-22-20000-1-1-1-10000000000002222-21-1-1-1-111-2111000-20-1-100010000
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χ23222222-12-12-122-1222-1-1-222-1-1-1-1-1-12-2-2-2-2-2-2-2-200-1-1-1-11111111110-222-2000011-1-1000000000000-2-22-22-1-1-111-1-1-21110002011000-10000
χ24222222-12-12-122-1222-1-1-222-1-1-1-1-1-12-2-2-2-2-2-2-2-200-1-1-1-11111111110-22-220000111100000000000022-2-22-11111-1-12-1-1-1000-20-1-100010000
χ2522222-12-1222-1222-1-12-12-1-12-1-12-12-1-1-122-1-1-1-122-1-1-1-1222-1-1-1-1-1-12220022-1-12200-1-1-1-1-1-122-1-1-1-1000-1-1200-1-1-1-10000220000000000-1-10
χ2622222-12-1222-1222-1-12-12-1-12-1-12-12-1-1-122-1-1-1-122-1-1-1-1222-1-1-1-1-1-12-2-20022-1-1-2-200-1-1-1-1-1-122-1-1-1-100011-20011110000-2-20000000000110
χ2722222-12-1222-1222-1-12-12-1-12-1-12-12-1-1-122-1-1-1-1-2-2-1-1-1-1222-1-1-1-1-1-1-22200-2-2112200111111-2-21111000-1-1200-1-1-1-10000-2-20000000000110
χ2822222-12-1222-1222-1-12-12-1-12-1-12-12-1-1-122-1-1-1-1-2-2-1-1-1-1222-1-1-1-1-1-1-2-2-200-2-211-2-200111111-2-2111100011-20011110000220000000000-1-10
χ2922222-12-1222-1222-1-12-1-2-1-12-1-12-12-111-2-2111122-1-1-1-1-2-2-2111111-22-200-2-21122001111-1-122-1-1-1-1000-11-200-1-11100002-20000000000-110
χ3022222-12-1222-1222-1-12-1-2-1-12-1-12-12-111-2-2111122-1-1-1-1-2-2-2111111-2-2200-2-211-2-2001111-1-122-1-1-1-10001-120011-1-10000-2200000000001-10
χ3122222-12-1222-1222-1-12-1-2-1-12-1-12-12-111-2-21111-2-2-1-1-1-1-2-2-211111122-20022-1-12200-1-1-1-111-2-21111000-11-200-1-1110000-2200000000001-10
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χ342222-12222-122-12-12-1-122-1-1-122-12-1-122-1-1-1-1-1-122-1-1-1-12-1-122-1-1-1-1200-2-2-1-12200-2-2-1-1-1-122-1-1-1-1-1-10010001100001-21100-20-20000101000
χ352222-12222-122-12-12-1-122-1-1-122-12-1-122-1-1-1-1-1-1-2-2-1-1-1-12-1-122-1-1-1-1-2002211-2-200221111-2-211111100-1000-1-10000-12-1-100-20-20000101000
χ362222-12222-122-12-12-1-122-1-1-122-12-1-122-1-1-1-1-1-1-2-2-1-1-1-12-1-122-1-1-1-1-200-2-211-2-200-2-21111-2-21111110010001100001-211002020000-10-1000
χ372222-12222-122-12-12-1-12-2-1-1-122-12-1-1-2-211111122-1-1-1-1-211-2-21111-2002-211-2-20022111122-1-1-1-1-1-100-1000-1-100001-2110020-20000-101000
χ382222-12222-122-12-12-1-12-2-1-1-122-12-1-1-2-211111122-1-1-1-1-211-2-21111-200-2211-2-200-2-2111122-1-1-1-1-1-1001000110000-12-1-100-202000010-1000
χ392222-12222-122-12-12-1-12-2-1-1-122-12-1-1-2-2111111-2-2-1-1-1-1-211-2-211112002-2-1-1220022-1-1-1-1-2-211111100-1000-1-100001-21100-202000010-1000
χ402222-12222-122-12-12-1-12-2-1-1-122-12-1-1-2-2111111-2-2-1-1-1-1-211-2-21111200-22-1-12200-2-2-1-1-1-1-2-2111111001000110000-12-1-10020-20000-101000
χ4122-2-22222-222-2-2-2-2-222202-2-22-2-2-22-2000000002i−2i22-2-2000000000000000000000000002i−2i2i−2i2i2i−2i−2i2-200000000000000000002-22i−2i000000
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χ4544444-2-2-2-24-2-24-24-2-2-214-2-2-211-21-2-2-2-244-2-2-2-2001111-2-2-2111111044000000-2-200000000000000000-2-2-20011110000000000000000000
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χ914-4-44-244-442-442-4-2-4-2-240222-4-4-242-20000000000-222-200000000000000−2i32i3000000−2i32i32i3−2i3000000000000000000000000000000000000000
χ924-4-44-244-442-442-4-2-4-2-240222-4-4-242-20000000000-222-2000000000000002i3−2i30000002i3−2i3−2i32i3000000000000000000000000000000000000000
χ934-4-44-2-24242-4-22-4-221-2-20-1-1222-2-221−2i32i300i3−i3−i3i3001-1-11000−2i32i3i3−i3−i3i300000−2i32i3000000i3−i3−i3i300003-3-330000000000000000000000000000000
χ944-4-44-2-24242-4-22-4-221-2-20-1-1222-2-221−2i32i300i3−i3−i3i3001-1-11000−2i32i3i3−i3−i3i3000002i3−2i3000000−i3i3i3−i30000-333-30000000000000000000000000000000
χ954-4-44-2-24242-4-22-4-221-2-20-1-1222-2-2212i3−2i300−i3i3i3−i3001-1-110002i3−2i3−i3i3i3−i300000−2i32i3000000i3−i3−i3i30000-333-30000000000000000000000000000000
χ964-4-44-2-24242-4-22-4-221-2-20-1-1222-2-2212i3−2i300−i3i3i3−i3001-1-110002i3−2i3−i3i3i3−i3000002i3−2i3000000−i3i3i3−i300003-3-330000000000000000000000000000000
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
χ9988-8-88-4-4-448-44-84-84-4-420-4442-24-2-44000000000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ10088-8-8-48-484-4-4-8444-8-42-40-44-2-44-2424000000000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-4-4-44-4-44444422202-2-22-2-2-22-200006i6i−6i−6i00-1-11100000−3i−3i3i3i00000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-4-4-44-4-44444422202-2-22-2-2-22-20000−6i−6i6i6i00-1-111000003i3i−3i−3i00000000000000000000000000000000000000000000000000000000
χ1038-88-88-4-444-8448-4-8-4-4-4204-4-4-224-24400000000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1048-88-8-4-4-444444-4-44-42220-222-22-2-2-2-20043−43−2323−232300-11-110−2323003−33−300000000000000000000000000000000000000000000000000000000
χ1058-88-8-4-4-444444-4-44-42220-222-22-2-2-2-200−434323−2323−2300-11-11023−2300−33−3300000000000000000000000000000000000000000000000000000000
χ1068-8-88-48-4-8-444844-4-8-42-4044-2442-4-2-400000000002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-44-444-444-442220-2-2-2-2-222-22−4i34i3002i3−2i3−2i32i300-111-10002i3−2i3−i3i3i3−i300000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-44-444-444-442220-2-2-2-2-222-224i3−4i300−2i32i32i3−2i300-111-1000−2i32i3i3−i3−i3i300000000000000000000000000000000000000000000000000000000

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