Finite Group Databasebeta

← Group #11722869

Character table — Group #11722869

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size11222222222444444444444666688888121212121212121212121212121212121212122424243636363636363672108
order1233346661212333666121212121212246636121212266666812121212242424242424242466622668242464
χ1111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-11111-1-1-1-1-1-1-1-11111-111-1-1-1-1-1
χ311111111111111111111111111111111-11-1-1111111111111111-1-1-1-1-1-1-1111-1-1
χ411111111111111111111111111111111-11-1-111-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-111
χ511111111111111111111111-1-1-1-1111111-111-1-11-1-1-1-111111111111-11-1-1-1-1-11-1
χ611111111111111111111111-1-1-1-1111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111-11
χ711111111111111111111111-1-1-1-111111-1-1-1-1-1-11-1-1-1-111111111-1-1-11-111-1-1-1-11
χ811111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1
χ922222-2222-2-2222222-2-2-2-2-2-22-22222-2-2-20200220-2-2-2-200000000000000000000
χ1022222-2222-2-2222222-2-2-2-2-2-2-22-2-222-2-2-20-200-2-20222200000000000000000000
χ112222-1222-1222-1-12-1-1-1-1-122222-1-1-1-1-1-1-122-1-1-1-102-1-1-1000000002-1-120-1-100000
χ122222-1222-1222-1-12-1-1-1-1-122222-1-1-1-1-1-1-1-2211-1-102-1-1-100000000-211-201100000
χ132222-1222-1222-1-12-1-1-1-1-1222-2-211-1-1-1-1-12-2-1-1110-2111000000002-1-1-201100000
χ142222-1222-1222-1-12-1-1-1-1-1222-2-211-1-1-1-1-1-2-211110-211100000000-21120-1-100000
χ152222-1-222-1-2-22-1-12-1-1111-2-2-22-2-1-1-1-111102−i3i3-1-10-2111000000000−i3i300−i3i300000
χ162222-1-222-1-2-22-1-12-1-1111-2-2-22-2-1-1-1-111102i3−i3-1-10-2111000000000i3−i300i3−i300000
χ172222-1-222-1-2-22-1-12-1-1111-2-2-2-2211-1-11110-2−i3i31102-1-1-1000000000−i3i300i3−i300000
χ182222-1-222-1-2-22-1-12-1-1111-2-2-2-2211-1-11110-2i3−i31102-1-1-1000000000i3−i300−i3i300000
χ19222-122-12222-12-1-1-12222-1-1-10000-1-1-1-1-12022002000022-1-1-1-1-1-1-1-1-10200000-10
χ20222-122-12222-12-1-1-12222-1-1-10000-1-1-1-1-1202200-20000-2-2111111-1-1-10-20000010
χ21222-122-12222-12-1-1-12222-1-1-10000-1-1-1-1-1-20-2-2002000022-1-1-1-1-1-11110-20000010
χ22222-122-12222-12-1-1-12222-1-1-10000-1-1-1-1-1-20-2-200-20000-2-21111111110200000-10
χ2322-12222-12-1-1-1-12-12-12-1-12-1-12222-1-12-1-10-100-1-12-12-1-1-1-122-1-1-1-100000002-1-100
χ2422-12222-12-1-1-1-12-12-12-1-12-1-12222-1-12-1-10-100-1-1-2-12-1-111-2-211110000000-21100
χ2522-12222-12-1-1-1-12-12-12-1-12-1-1-2-2-2-2-1-12-1-101001121-211-1-122-1-1-1-10000000-21100
χ2622-12222-12-1-1-1-12-12-12-1-12-1-1-2-2-2-2-1-12-1-1010011-21-21111-2-2111100000002-1-100
χ2722-122-22-1211-1-12-12-1-211-2112-222-1-1-2110-100-1-101-2113−30033−3−3000000003−300
χ2822-122-22-1211-1-12-12-1-211-2112-222-1-1-2110-100-1-101-211−3300−3−33300000000−3300
χ2922-122-22-1211-1-12-12-1-211-211-22-2-2-1-1-2110100110-12-1-13−30033−3−300000000−3300
χ3022-122-22-1211-1-12-12-1-211-211-22-2-2-1-1-2110100110-12-1-1−3300−3−333000000003−300
χ31444-24-4-244-4-4-24-2-2-24-4-4-42220000-2-22220000000000000000000000000000000
χ32444-2-24-24-244-2-21-21-2-2-2-2-2-2-200001111140-2-2000000000000000-211000000000
χ33444-2-24-24-244-2-21-21-2-2-2-2-2-2-2000011111-40220000000000000002-1-1000000000
χ34444-2-2-4-24-2-4-4-2-21-21-2222222000011-1-1-100−2i32i30000000000000000i3−i3000000000
χ35444-2-2-4-24-2-4-4-2-21-21-2222222000011-1-1-1002i3−2i30000000000000000−i3i3000000000
χ3644-24-244-2-2-2-2-21-2-2-21-2114-2-244-2-211-2110-200110-2-21100000000000000000000
χ3744-24-244-2-2-2-2-21-2-2-21-2114-2-2-4-42211-2110200-1-1022-1-100000000000000000000
χ3844-24-2-44-2-222-21-2-2-212-1-1-4224-4-2-2112-1-10-20011022-1-100000000000000000000
χ3944-24-2-44-2-222-21-2-2-212-1-1-422-4422112-1-10200-1-10-2-21100000000000000000000
χ4044-2-244-2-24-2-21-2-21-2-24-2-2-211000011-21100000040000-2-2-2-21111000000000000
χ4144-2-244-2-24-2-21-2-21-2-24-2-2-211000011-211000000-400002222-1-1-1-1000000000000
χ4244-2-24-4-2-24221-2-21-2-2-4222-1-10000112-1-10000000000023−2300−3−333000000000000
χ4344-2-24-4-2-24221-2-21-2-2-4222-1-10000112-1-100000000000−23230033−3−3000000000000
χ444-44440-4-4-400444-4-4-400000000004-40000000000000000000000000000000000
χ454-444-20-4-42004-2-2-42200000000−2i32i3-220000000−2i32i30000000000000000000000000
χ464-444-20-4-42004-2-2-422000000002i3−2i3-2200000002i3−2i30000000000000000000000000
χ474-44-2402-4-400-24-222-40000000000-220000000000000000i6−i6i6−i6i6−i6000000000000
χ484-44-2402-4-400-24-222-40000000000-220000000000000000−i6i6−i6i6−i6i6000000000000
χ494-4-2440-42-423−23-2-242-42023−23023−230000-22023−230000000000000000000000000000000
χ504-4-2440-42-4−2323-2-242-420−23230−23230000-220−23230000000000000000000000000000000
χ514-4-24-20-42223−23-21-222-10−33023−2300−2i32i31-10−330000i3−i30003i−3i00000000000000000000
χ524-4-24-20-42223−23-21-222-10−33023−23002i3−2i31-10−330000−i3i3000−3i3i00000000000000000000
χ534-4-24-20-422−2323-21-222-103−30−232300−2i32i31-103−30000i3−i3000−3i3i00000000000000000000
χ544-4-24-20-422−2323-21-222-103−30−2323002i3−2i31-103−30000−i3i30003i−3i00000000000000000000
χ554-4-2-24022-423−231-2-2-122023−230−3300001-10−330000000000000i6−i6−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23000000000000
χ564-4-2-24022-423−231-2-2-122023−230−3300001-10−330000000000000−i6i62ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23000000000000
χ574-4-2-24022-4−23231-2-2-1220−232303−300001-103−30000000000000i6−i6ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23000000000000
χ584-4-2-24022-4−23231-2-2-1220−232303−300001-103−30000000000000−i6i6−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23000000000000
χ5988-4-4-48-4-4-4-4-4222222-422-4220000-1-12-1-10000000000000000000000000000000
χ6088-4-4-4-8-4-4-4442222224-2-24-2-20000-1-1-2110000000000000000000000000000000
χ618-88-4-404-8400-4-424-2400000000002-20000000000000000000000000000000000
χ628-8-4-4-4044443−43222-2-2-20−23230−23230000-1103−30000000000000000000000000000000
χ638-8-4-4-40444−4343222-2-2-2023−23023−230000-110−330000000000000000000000000000000

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