Finite Group Databasebeta

← Group #13170689

Character table — Group #13170689

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size1122222222222224444444444444444444444466888888888888121212121212121212121212121212121212121212121212121212121218181818242424242424242424242424363636363636363672727272108108
order12233344666661212333666666666121212121212121212121288366661212121212121224446681212121212122424242424242424242424242424242422446661212121212121212122444661212612121288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-111111-1-1-1-11111111111111111-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-111-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-111-1-11-1-111111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-1-1-111-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-11-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ511111111111111111111111111111111111111-1-1111111111111111111-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1
χ611111111111111111111111111111111111111-1-111111111111111-1-111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111-1-1-1-1-1-11111
χ711111111111111111111111111111111111111-1-1111111111111-1-111-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-111-1-111
χ811111111111111111111111111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ911-1111-11-1-1111-1-1111-1-1-1-1-1-11111-1-1-1-1-1-11111111-1-1-1111-111-1-11-11-111-1-1-111-1-111111111-1-1-1-1-1-1-1-11-11-1111-11-1-1-111-1-11-11-11-11-11-11-11-1
χ1011-1111-11-1-1111-1-1111-1-1-1-1-1-11111-1-1-1-1-1-11111111-1-1-1111-111-1-11-1-1111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-11111-1-11-1-1-1-1111-1-11-11-111-1-11-11
χ1111-1111-11-1-1111-1-1111-1-1-1-1-1-11111-1-1-1-1-1-11111111-1-1-1111-111-1-1-111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-11-11-1-1-111-11111-1-1-111-1-11-11-111-1-11
χ1211-1111-11-1-1111-1-1111-1-1-1-1-1-11111-1-1-1-1-1-11111111-1-1-1111-111-1-1-11-11-1-1-111-1-11111111111-1-1-1-1-1-1-1-11-11-1-1-1-11-1111-1-111-11-111-11-1-11-111-1
χ1311-1111-11-1-1111-1-1111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11-1-1-1111-111-1-11-11-1111-1-111-1-1-1-1-1-1-1-1-1-1111111111-11-1111-11-1-1-111-1-1-11-111-11-1-11-11-11
χ1411-1111-11-1-1111-1-1111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11-1-1-1111-111-1-11-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111-11-11111-1-11-1-1-1-111-111-1-11-11-111-11-1
χ1511-1111-11-1-1111-1-1111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11-1-1-1111-111-1-1-111-1-1-111111-1-1-1-1-1-1-1-1-1-111111111-11-11-1-1-111-11111-1-11-1-11-11-111-1-111-1
χ1611-1111-11-1-1111-1-1111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11-1-1-1111-111-1-1-11-11-1-1111-1-111-1-1-1-1-1-1-1-1111111111-11-1-1-1-11-1111-1-1111-11-11-11-11-11-1-11
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χ2222222-122222-12222-1-12-122-1-12-1-1-1-1222-1-1222200-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211011111100000000000000002222-211-2-2-21111110000-1-1-1-1000000
χ2322222-1-2-2222-12-2-22-1-12-122-1-12-1-111-2-2-211-2-2-2-200-1-1-1-1-111111110000−i3i30−i3i3−i3i3−i3i300000000000000002-2-220−i3i3000−i3i3−i3i3−i3i30000-111-1000000
χ2422222-1-2-2222-12-2-22-1-12-122-1-12-1-111-2-2-211-2-2-2-200-1-1-1-1-111111110000−i3i30−i3i3i3−i3i3−i30000000000000000-222-20−i3i3000−i3i3i3−i3i3−i300001-1-11000000
χ2522222-1-2-2222-12-2-22-1-12-122-1-12-1-111-2-2-211-2-2-2-200-1-1-1-1-111111110000i3−i30i3−i3−i3i3−i3i30000000000000000-222-20i3−i3000i3−i3−i3i3−i3i300001-1-11000000
χ2622222-1-2-2222-12-2-22-1-12-122-1-12-1-111-2-2-211-2-2-2-200-1-1-1-1-111111110000i3−i30i3−i3i3−i3i3−i300000000000000002-2-220i3−i3000i3−i3i3−i3i3−i30000-111-1000000
χ272222-122222-122-1-1-12-1-12-1-122-1-12222-1-1-1-1-12-1-122-1-1-1-1-1-122-1-1-1-1220022222000022-1-1-1-1-1-122-1-1-1-1-1-10000-1-1-1-100-1-1000022000000-1-10000
χ282222-122222-122-1-1-12-1-12-1-122-1-12222-1-1-1-1-12-1-122-1-1-1-1-1-122-1-1-1-1-2-200-2-22-2-2000022-1-1-1-1-1-122-1-1-1-1-1-10000111100110000-2-2000000110000
χ292222-122222-122-1-1-12-1-12-1-122-1-12222-1-1-1-1-12-1-1-2-2-1-1-1-1-1-122-1-1-1-1220022-2220000-2-2111111-2-21111110000-1-1-1-100-1-10000-2-2000000110000
χ302222-122222-122-1-1-12-1-12-1-122-1-12222-1-1-1-1-12-1-1-2-2-1-1-1-1-1-122-1-1-1-1-2-200-2-2-2-2-20000-2-2111111-2-2111111000011110011000022000000-1-10000
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χ32222-12222-1-122-122-1-1222-1-1-1-1-12-122-1-1-1222-1-1-122-12-1-1-12-1-1-1-1-1-100-2-200200-2-2-2-2-1-122-1-1-1-1-1-122-1-1-1-1000000001100111100-2-20000001100
χ33222-12222-1-122-122-1-1222-1-1-1-1-12-122-1-1-1222-1-1-1-2-2-12-1-1-12-1-1-1-1-1-1002200-200222211-2-2111111-2-2111100000000-1-100-1-1-1-100-2-20000001100
χ34222-12222-1-122-122-1-1222-1-1-1-1-12-122-1-1-1222-1-1-1-2-2-12-1-1-12-1-1-1-1-1-100-2-200-200-2-2-2-211-2-2111111-2-2111100000000110011110022000000-1-100
χ3522-22222-2-2-222222222-2-2-2-2-2-2222-2222222-2-2-2-2002-2-2-22-2-22-2-2220000000000000000000000000000022-2-2000000000000000022-2-2000000
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χ3722-222-12-2-2-22-12222-1-1-21-2-2112-1-11-1222-1-1-2-2-2-200-1111-111-111-1-10000−i3i30i3−i3−i3i3i3−i3000000000000000022-2-20−i3i3000i3−i3−i3i3i3−i30000-1-111000000
χ3822-222-12-2-2-22-12222-1-1-21-2-2112-1-11-1222-1-1-2-2-2-200-1111-111-111-1-10000−i3i30i3−i3i3−i3−i3i30000000000000000-2-2220−i3i3000i3−i3i3−i3−i3i3000011-1-1000000
χ3922-222-12-2-2-22-12222-1-1-21-2-2112-1-11-1222-1-1-2-2-2-200-1111-111-111-1-10000i3−i30−i3i3−i3i3i3−i30000000000000000-2-2220i3−i3000−i3i3−i3i3i3−i3000011-1-1000000
χ4022-222-12-2-2-22-12222-1-1-21-2-2112-1-11-1222-1-1-2-2-2-200-1111-111-111-1-10000i3−i30−i3i3i3−i3−i3i3000000000000000022-2-20i3−i3000−i3i3i3−i3−i3i30000-1-111000000
χ4122-222-1-22-2-22-12-2-22-1-1-21-2-2112-1-1-11-2-2-211222200-1111-1-1-11-1-1112-22-2-1-1011-1-11100000000000000002-22-22-1-1-22-211-1-1110000-11-11000000
χ4222-222-1-22-2-22-12-2-22-1-1-21-2-2112-1-1-11-2-2-211222200-1111-1-1-11-1-1112-2-22-1-101111-1-10000000000000000-22-222-1-1-2-221111-1-100001-11-1000000
χ4322-222-1-22-2-22-12-2-22-1-1-21-2-2112-1-1-11-2-2-211222200-1111-1-1-11-1-111-222-2110-1-1-1-1110000000000000000-22-22-21122-2-1-1-1-11100001-11-1000000
χ4422-222-1-22-2-22-12-2-22-1-1-21-2-2112-1-1-11-2-2-211222200-1111-1-1-11-1-111-22-22110-1-111-1-100000000000000002-22-2-2112-22-1-111-1-10000-11-11000000
χ4522-22-12-22-2-2-12211-12-11-211-2-2-1-122-2-21111-12-1-122-1111-1-12-2-1-1112-20022-2-2-2000022-1-1-1-1-1-1-2-21111110000-1-1-11001100002-2000000-110000
χ4622-22-12-22-2-2-12211-12-11-211-2-2-1-122-2-21111-12-1-122-1111-1-12-2-1-111-2200-2-2-222000022-1-1-1-1-1-1-2-21111110000111-100-1-10000-220000001-10000
χ4722-22-12-22-2-2-12211-12-11-211-2-2-1-122-2-21111-12-1-1-2-2-1111-1-12-2-1-1112-200222-2-20000-2-211111122-1-1-1-1-1-10000-1-1-1100110000-220000001-10000
χ4822-22-12-22-2-2-12211-12-11-211-2-2-1-122-2-21111-12-1-1-2-2-1111-1-12-2-1-111-2200-2-22220000-2-211111122-1-1-1-1-1-10000111-100-1-100002-2000000-110000
χ4922-2-122-221122-1-2-2-1-12-2-21111-12-12-2111-2-22-1-1-122-1-211-12-11-1-111002-200-20022-2-2-1-122-1-1-1-111-2-2111100000000-1100-1-111002-2000000-1100
χ5022-2-122-221122-1-2-2-1-12-2-21111-12-12-2111-2-22-1-1-122-1-211-12-11-1-11100-2200-200-2-222-1-122-1-1-1-111-2-21111000000001-10011-1-100-220000001-100
χ5122-2-122-221122-1-2-2-1-12-2-21111-12-12-2111-2-22-1-1-1-2-2-1-211-12-11-1-111002-20020022-2-211-2-21111-1-122-1-1-1-100000000-1100-1-11100-220000001-100
χ5222-2-122-221122-1-2-2-1-12-2-21111-12-12-2111-2-22-1-1-1-2-2-1-211-12-11-1-11100-2200200-2-22211-2-21111-1-122-1-1-1-1000000001-10011-1-1002-2000000-1100
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χ864-404-2400002-4-4−2323-24-200000022-4000−2323−23230000−2222-2000200000−23230000000000000−22222−22−22−2006−66−66−6000000000000000000000000000000
χ874-40-24400−2i32i3-4-4200-2-2400−2i32i3−2i32i32-420000000000022−22-20−2i32i3200000000000000000000−2222−22−22−22i6−i600i6−i6−i6i6000000000000000000000000000000
χ884-40-24400−2i32i3-4-4200-2-2400−2i32i3−2i32i32-4200000000000−2222-20−2i32i32000000000000000000002−2−22222−22−2−i6i600−i6i6i6−i6000000000000000000000000000000
χ894-40-244002i3−2i3-4-4200-2-24002i3−2i32i3−2i32-420000000000022−22-202i3−2i3200000000000000000000−2222−22−22−22−i6i600−i6i6i6−i6000000000000000000000000000000
χ904-40-244002i3−2i3-4-4200-2-24002i3−2i32i3−2i32-4200000000000−2222-202i3−2i32000000000000000000002−2−22222−22−2i6−i600i6−i6−i6i6000000000000000000000000000000
χ914-40-2-2400−2i32i32-4223−231-2-200i3−i3−2i32i3-122000−3323−23003i−3i22−2210i3−i3-10003i−3i−330000000000000−22−22ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23i6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000000
χ924-40-2-2400−2i32i32-4223−231-2-200i3−i3−2i32i3-122000−3323−23003i−3i−222210i3−i3-10003i−3i−3300000000000002−22−2−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000000
χ934-40-2-2400−2i32i32-42−23231-2-200i3−i3−2i32i3-1220003−3−232300−3i3i22−2210i3−i3-1000−3i3i3−30000000000000−22−22−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23i6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000000
χ944-40-2-2400−2i32i32-42−23231-2-200i3−i3−2i32i3-1220003−3−232300−3i3i−222210i3−i3-1000−3i3i3−300000000000002−22−22ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ23−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000000
χ954-40-2-24002i3−2i32-4223−231-2-200−i3i32i3−2i3-122000−3323−2300−3i3i22−2210−i3i3-1000−3i3i−330000000000000−22−22−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000000
χ964-40-2-24002i3−2i32-4223−231-2-200−i3i32i3−2i3-122000−3323−2300−3i3i−222210−i3i3-1000−3i3i−3300000000000002−22−22ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ23i6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000000
χ974-40-2-24002i3−2i32-42−23231-2-200−i3i32i3−2i3-1220003−3−2323003i−3i22−2210−i3i3-10003i−3i3−30000000000000−22−22ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000000
χ984-40-2-24002i3−2i32-42−23231-2-200−i3i32i3−2i3-1220003−3−2323003i−3i−222210−i3i3-10003i−3i3−300000000000002−22−2−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23i6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000000
χ99888-4-4-488-4-4-4-4-4-4-4222-4-42222222-4-4-42222-4-42200-12-1-1-1222-1-1-1-100000000000000000000000000000000000000000000000000000000000
χ100888-4-4-4-8-8-4-4-4-4-444222-4-42222222444-2-2-2-244-2-200-12-1-1-1-2-2-2111100000000000000000000000000000000000000000000000000000000000
χ10188-8-4-4-48-844-4-4-4-4-422244-2-2-2-22224-4-4222244-2-200-1-211-1-2-2211-1-100000000000000000000000000000000000000000000000000000000000
χ10288-8-4-4-4-8844-4-4-44422244-2-2-2-2222-444-2-2-2-2-4-42200-1-211-122-2-1-11100000000000000000000000000000000000000000000000000000000000
χ1038-8088-40000-84-8008-4-4000000-8440000000000000-40004000000000000000000000000000000000000000000000000000000000000000000
χ1048-808-4-4000044-843−43-4-420000004-2400043−43−23230000002000-200000−232300000000000000000000000000000000000000000000000000000000000
χ1058-808-4-4000044-8−4343-4-420000004-24000−434323−230000002000-20000023−2300000000000000000000000000000000000000000000000000000000000
χ1068-80-48-400−4i34i3-84400-42-400−4i34i32i3−2i344-20000000000000202i3−2i3-2000000000000000000000000000000000000000000000000000000000000000000
χ1078-80-48-4004i3−4i3-84400-42-4004i3−4i3−2i32i344-2000000000000020−2i32i3-2000000000000000000000000000000000000000000000000000000000000000000
χ1088-80-4-4-400−4i34i344443−43222002i3−2i32i3−2i3-2-2-2000−2323−2323006i−6i00-10−i3i31000−3i3i3−300000000000000000000000000000000000000000000000000000000000
χ1098-80-4-4-400−4i34i3444−4343222002i3−2i32i3−2i3-2-2-200023−2323−2300−6i6i00-10−i3i310003i−3i−3300000000000000000000000000000000000000000000000000000000000
χ1108-80-4-4-4004i3−4i344443−4322200−2i32i3−2i32i3-2-2-2000−2323−232300−6i6i00-10i3−i310003i−3i3−300000000000000000000000000000000000000000000000000000000000
χ1118-80-4-4-4004i3−4i3444−434322200−2i32i3−2i32i3-2-2-200023−2323−23006i−6i00-10i3−i31000−3i3i−3300000000000000000000000000000000000000000000000000000000000

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