Finite Group Databasebeta

← Group #13155697

Character table — Group #13155697

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11112222222222222244444444444444444444448888888888881212121212121212121212121212121212121212121224242424242424242424242424242424363636363636363636365454545472727272
order1222333446666666663336666666661212121212121212121236661212121212121212444488242424242424242424242424242424241212121212121212121212121212121244448824242424444412121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111-1-111111111111111111111-1-111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ4111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-111-1-1-1-1-1-11111-1-111
χ51111111111111111111111111111111111111111111111111111-1-111111111111111111111-1-111-1-111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-111
χ61111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1
χ71111111111111111111111111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ81111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111
χ911-1-1111-11-1-1-1-1111-1-1111-1-1-1-1-1-111111-111-1-1-1-111-1-1111-1-111-1-11-11-1i−iiiiiiiii−i−i−i−i−i−i−i−i1-11-11-11-111-1-111-1-1i−ii−i1-111-1-1ii−i−ii−ii−i
χ1011-1-1111-11-1-1-1-1111-1-1111-1-1-1-1-1-111111-111-1-1-1-111-1-1111-1-111-1-11-11-1−ii−i−i−i−i−i−i−i−iiiiiiiii1-11-11-11-111-1-111-1-1−ii−ii1-111-1-1−i−iii−ii−ii
χ1111-1-1111-11-1-1-1-1111-1-1111-1-1-1-1-1-111111-111-1-1-1-111-1-1111-1-111-1-11-1-11i−iiiiiiiii−i−i−i−i−i−i−i−i1-1-111-1-1111-1-1-1-111i−i−ii-11-1-111−i−iiii−i−ii
χ1211-1-1111-11-1-1-1-1111-1-1111-1-1-1-1-1-111111-111-1-1-1-111-1-1111-1-111-1-11-1-11−ii−i−i−i−i−i−i−i−iiiiiiiii1-1-111-1-1111-1-1-1-111−iii−i-11-1-111ii−i−i−iii−i
χ1311-1-1111-11-1-1-1-1111-1-1111-1-1-1-1-1-111111-111-1-1-1-111-1-1111-1-111-1-1-111-1i−iiiiiiiii−i−i−i−i−i−i−i−i-111-1-111-1-1-11111-1-1−iii−i-11-1-111−i−iii−iii−i
χ1411-1-1111-11-1-1-1-1111-1-1111-1-1-1-1-1-111111-111-1-1-1-111-1-1111-1-111-1-1-111-1−ii−i−i−i−i−i−i−i−iiiiiiiii-111-1-111-1-1-11111-1-1i−i−ii-11-1-111ii−i−ii−i−ii
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χ1611-1-1111-11-1-1-1-1111-1-1111-1-1-1-1-1-111111-111-1-1-1-111-1-1111-1-111-1-1-11-11−ii−i−i−i−i−i−i−i−iiiiiiiii-11-11-11-11-1-111-1-111i−ii−i1-111-1-1−i−iiii−ii−i
χ172222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-20000000000000000000000000000000000000000000000002-22-20000
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χ2522222-122222-12-122-12-12-1-1-122-1-1-1-12-122-1-1-12-1-12-1-1-1-1-12-12-1-1-1-1-2-20022-1-122-1-1-1-1-1-122-1-1-1-11100-2-20011110000-2-20000000000001100
χ2622222-122222-12-122-12-12-1-1-122-1-1-1-12-122-1-1-12-1-12-1-1-1-1-12-12-1-1-1-1-2-200-2-211-2-2111111-2-211111100-2-2001111000022000000000000-1-100
χ272222-12222-1-12222-122-1-12-1-1-1-1222-1-122-1222222-1-1-1-1-1-1-1-1-1-1-1-1-122220000000000000000002222-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-100000000
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χ292222-12222-1-12222-122-1-12-1-1-1-1222-1-122-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222000000000000000000-2-22211-1-11111-1-1-1-10000-2-2111100000000
χ302222-12222-1-12222-122-1-12-1-1-1-1222-1-122-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2000000000000000000-2-2-2-2111111111111000022-1-1-1-100000000
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χ3622-2-222-1-22-2-2-212-12-212-1-1-2-21111-12-12-1-2-1-1-21112-111-12-1-21-1-11100-22−2i2i−2i−2iiiiiii2i2i−i−i−i−i−i−i001-100-22000011-1-1002i−2i000000000000−ii
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χ3822-2-22-12-22-2-21-2-1221-2-12-111-2-211-1-12-12-2-1-11-2112-111-1-121-2-1-1112-200−2i2iii−2i−2iiiii−i−i2i2i−i−i−i−i-11002-200-1-1110000−2i2i000000000000i−i00
χ3922-2-22-12-22-2-21-2-1221-2-12-111-2-211-1-12-12-2-1-11-2112-111-1-121-2-1-111-22002i−2i−i−i2i2i−i−i−i−iii−2i−2iiiii1-100-220011-1-10000−2i2i000000000000i−i00
χ4022-2-22-12-22-2-21-2-1221-2-12-111-2-211-1-12-12-2-1-11-2112-111-1-121-2-1-111-2200−2i2iii−2i−2iiiii−i−i2i2i−i−i−i−i1-100-220011-1-100002i−2i000000000000−ii00
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χ894-4-444-2400-44242-4-4-2-4-24-22-2-442-222-40000000000-22-22000000000000006−6006−6−66−6600−666−60000000000000000000000000000000000
χ904-4-444-2400-44242-4-4-2-4-24-22-2-442-222-40000000000-22-2200000000000000−6600−666−66−6006−6−660000000000000000000000000000000000
χ914-4-444-2-200-442-222-4-22-2-212-22-2-11-1220003i−3i00−3i3i01-11-100003i−3i−3i3i0000006−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ130000000000000000000000000000000000
χ924-4-444-2-200-442-222-4-22-2-212-22-2-11-1220003i−3i00−3i3i01-11-100003i−3i−3i3i000000−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ136−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ130000000000000000000000000000000000
χ934-4-444-2-200-442-222-4-22-2-212-22-2-11-122000−3i3i003i−3i01-11-10000−3i3i3i−3i0000006−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ230000000000000000000000000000000000
χ944-4-444-2-200-442-222-4-22-2-212-22-2-11-122000−3i3i003i−3i01-11-10000−3i3i3i−3i000000−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ236−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ230000000000000000000000000000000000
χ954-4-44-244002-2-44-4-424-4-2-242-22-2-44-4220000000000-22-220000000000000000000000000000000000000000000000000000i6−i6−i6i600000000
χ964-4-44-244002-2-44-4-424-4-2-242-22-2-44-4220000000000-22-220000000000000000000000000000000000000000000000000000−i6i6i6−i600000000
χ978888-4-4-488-4-4-4-4-4-4-4-4-4222222222222-4-4-422-4-422-4-1-1-1-12222-1-1-1-100000000000000000000000000000000000000000000000000000000
χ988888-4-4-4-8-8-4-4-4-4-4-4-4-4-4222222222222444-2-244-2-24-1-1-1-1-2-2-2-2111100000000000000000000000000000000000000000000000000000000
χ9988-8-8-4-4-48-84444-4-4-444222-2-2-2-2-2-222244-4-2-2-4-4224-111-1-2-22211-1-100000000000000000000000000000000000000000000000000000000
χ10088-8-8-4-4-4-884444-4-4-444222-2-2-2-2-2-2222-4-442244-2-2-4-111-122-2-2-1-11100000000000000000000000000000000000000000000000000000000
χ1018-88-8-48-400-4484-844-8-4-42-4-442-2-4444-2000000000022-2-20000000000000000000000000000000000000000000000000000000000000000
χ1028-88-8-4-4800-44-4-84-84482-4-42-2-44-444-24000000000022-2-20000000000000000000000000000000000000000000000000000000000000000
χ1038-88-8-4-4-400-44-444444-42222-22-22-2-2-2-20006i−6i006i−6i0-1-1110000−3i3i−3i3i00000000000000000000000000000000000000000000000000000000
χ1048-88-8-4-4-400-44-444444-42222-22-22-2-2-2-2000−6i6i00−6i6i0-1-11100003i−3i3i−3i00000000000000000000000000000000000000000000000000000000
χ1058-8-88-48-4004-4-8-4-84484-42-44-4-224-444-200000000002-22-20000000000000000000000000000000000000000000000000000000000000000
χ1068-8-88-4-48004-4484-84-4-82-4-4-224-44-44-2400000000002-22-20000000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-4004-44-4444-44222-22-22-22-2-2-20006i−6i00−6i6i0-11-110000−3i3i3i−3i00000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-4004-44-4444-44222-22-22-22-2-2-2000−6i6i006i−6i0-11-1100003i−3i−3i3i00000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.