Finite Group Databasebeta

← Group #11721055

Character table — Group #11721055

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size111122222222226666666699991212121212121212121212121818181818181818181818181818181818183636363636363636
order12442346661212121233661212121288883666661212121212122244888888242424242424242466121224242424
χ11111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111-11-1-1-11-1-1111111111111111-1-1-1-11-1-111-1-11-11-1-1-111-1-11111-1-1-1-11-11-111-1-1
χ61111-11-1-1-11-1-1111111111111111-1-1-1-11-1-111-1-1-11-11-1-1-1-1111111-1-1-1-1-11-11-1-111
χ71111-11-1-1-11-1-11111111111-1-1-1-11-1-1-1-11-1-111-1-11-11-111-1-111-1-1-1-111111-11-1-1-111
χ81111-11-1-1-11-1-11111111111-1-1-1-11-1-1-1-11-1-111-1-1-11-111111-1-1-1-1-1-11111-11-1111-1-1
χ911-1-111-1111-1-1-1-11111-1-1-1-1ii−i−i111111-1-1-1-1-1-11-1-11i−ii−ii−iii−i−iii−i−i1-1-11i−ii−i
χ1011-1-111-1111-1-1-1-11111-1-1-1-1ii−i−i111111-1-1-1-1-1-1-111-1i−i−ii−iiii−i−iii−i−i-111-1−ii−ii
χ1111-1-111-1111-1-1-1-11111-1-1-1-1−i−iii111111-1-1-1-1-1-11-1-11−ii−ii−ii−i−iii−i−iii1-1-11−ii−ii
χ1211-1-111-1111-1-1-1-11111-1-1-1-1−i−iii111111-1-1-1-1-1-1-111-1−iii−ii−i−i−iii−i−iii-111-1i−ii−i
χ1311-1-1-111-1-1111-1-11111-1-1-1-1ii−i−i1-1-1-1-1111-1-11111-1-1−iii−i−iiii−i−i−i−iii11-1-1i−i−ii
χ1411-1-1-111-1-1111-1-11111-1-1-1-1ii−i−i1-1-1-1-1111-1-111-1-111−ii−iii−iii−i−i−i−iii-1-111−iii−i
χ1511-1-1-111-1-1111-1-11111-1-1-1-1−i−iii1-1-1-1-1111-1-11111-1-1i−i−iii−i−i−iiiii−i−i11-1-1−iii−i
χ1611-1-1-111-1-1111-1-11111-1-1-1-1−i−iii1-1-1-1-1111-1-111-1-111i−ii−i−ii−i−iiiii−i−i-1-111i−i−ii
χ17222222222222222-12-1-1-1220000-12-1-1-1-12-1-1-1-1-1222200000000000000-1-1-1-10000
χ18222222222222222-12-1-1-1220000-12-1-1-1-12-1-1-1-1-1-2-2-2-20000000000000011110000
χ1922222222222222-12-1222-1-10000-1-12-1-1-1-12-1-1-1-10000002222000000000000-1-1-1-1
χ2022222222222222-12-1222-1-10000-1-12-1-1-1-12-1-1-1-1000000-2-2-2-20000000000001111
χ212222-22-2-2-22-2-2222-12-1-1-1220000-1-2111-1-21-1-1112-22-200000000000000-11-110000
χ222222-22-2-2-22-2-2222-12-1-1-1220000-1-2111-1-21-1-111-22-22000000000000001-11-10000
χ232222-22-2-2-22-2-222-12-1222-1-10000-11-211-11-2-1-11100000022-2-2000000000000-1-111
χ242222-22-2-2-22-2-222-12-1222-1-10000-11-211-11-2-1-111000000-2-22200000000000011-1-1
χ2522-2-222-2222-2-2-2-22-12-111-2-20000-12-1-1-1-1-2111112-2-2200000000000000-111-10000
χ2622-2-222-2222-2-2-2-22-12-111-2-20000-12-1-1-1-1-211111-222-2000000000000001-1-110000
χ2722-2-222-2222-2-2-2-2-12-12-2-2110000-1-12-1-1-11-211110000002i−2i2i−2i000000000000−ii−ii
χ2822-2-222-2222-2-2-2-2-12-12-2-2110000-1-12-1-1-11-21111000000−2i2i−2i2i000000000000i−ii−i
χ2922-2-2-222-2-2222-2-22-12-111-2-20000-1-2111-12-111-1-122-2-200000000000000-1-1110000
χ3022-2-2-222-2-2222-2-22-12-111-2-20000-1-2111-12-111-1-1-2-2220000000000000011-1-10000
χ3122-2-2-222-2-2222-2-2-12-12-2-2110000-11-211-1-1211-1-10000002i−2i−2i2i000000000000−iii−i
χ3222-2-2-222-2-2222-2-2-12-12-2-2110000-11-211-1-1211-1-1000000−2i2i2i−2i000000000000i−i−ii
χ332-22i−2i02000-2002i−2i22-2-22i−2i2i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1320000-2002i−2i0000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000
χ342-22i−2i02000-2002i−2i22-2-22i−2i2i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1320000-2002i−2i000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000
χ352-2−2i2i02000-200−2i2i22-2-2−2i2i−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2320000-200−2i2i000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000
χ362-2−2i2i02000-200−2i2i22-2-2−2i2i−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2320000-200−2i2i0000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000
χ3744444444444444-2-2-2-2-2-2-2-200001-2-2111-2-2111100000000000000000000000000
χ384444-44-4-4-44-4-444-2-2-2-2-2-2-2-20000122-1-112211-1-100000000000000000000000000
χ3944-4-444-4444-4-4-4-4-2-2-2-2222200001-2-211122-1-1-1-100000000000000000000000000
χ4044-4-4-444-4-4444-4-4-2-2-2-222220000122-1-11-2-2-1-11100000000000000000000000000
χ414-44i−4i04000-4004i−4i4-2-42−2i2i4i−4i0000-20000200−2i2i0000000000000000000000000000
χ424-44i−4i04000-4004i−4i-242-44i−4i−2i2i0000-20000200−2i2i0000000000000000000000000000
χ434-44i−4i04000-4004i−4i-2-222−2i2i−2i2i00001003-3-100i−i3i−3i00000000000000000000000000
χ444-44i−4i04000-4004i−4i-2-222−2i2i−2i2i0000100-33-100i−i−3i3i00000000000000000000000000
χ454-4−4i4i04000-400−4i4i4-2-422i−2i−4i4i0000-200002002i−2i0000000000000000000000000000
χ464-4−4i4i04000-400−4i4i-242-4−4i4i2i−2i0000-200002002i−2i0000000000000000000000000000
χ474-4−4i4i04000-400−4i4i-2-2222i−2i2i−2i00001003-3-100−ii−3i3i00000000000000000000000000
χ484-4−4i4i04000-400−4i4i-2-2222i−2i2i−2i0000100-33-100−ii3i−3i00000000000000000000000000
χ4966666-36-3-3-3-3-3-3-30000000022220000000000000000220000-1-1-1-1-1-1-1-100000000
χ5066666-36-3-3-3-3-3-3-300000000-2-2-2-20000000000000000-2-200001111111100000000
χ516666-6-3-633-333-3-30000000022220000000000000000-2-20000-1-1-1-1111100000000
χ526666-6-3-633-333-3-300000000-2-2-2-200000000000000002200001111-1-1-1-100000000
χ5366-6-66-3-6-3-3-33333000000002i2i−2i−2i00000000000000002i−2i0000−i−iii−i−iii00000000
χ5466-6-66-3-6-3-3-3333300000000−2i−2i2i2i0000000000000000−2i2i0000ii−i−iii−i−i00000000
χ5566-6-6-6-3633-3-3-333000000002i2i−2i−2i0000000000000000−2i2i0000−i−iiiii−i−i00000000
χ5666-6-6-6-3633-3-3-33300000000−2i−2i2i2i00000000000000002i−2i0000ii−i−i−i−iii00000000
χ576-66i−6i0-30−3i33i3333−33−3i3i000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000000000000000−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000
χ586-66i−6i0-30−3i33i3333−33−3i3i00000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000000000000000ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000000
χ596-66i−6i0-303i3−3i33−3333−3i3i000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000000000000000−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000000
χ606-66i−6i0-303i3−3i33−3333−3i3i00000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000000000000000ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000
χ616-6−6i6i0-30−3i33i33−33333i−3i00000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000000000000000ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300000000
χ626-6−6i6i0-30−3i33i33−33333i−3i000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000000000000000−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300000000
χ636-6−6i6i0-303i3−3i3333−333i−3i00000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000000000000000ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300000000
χ646-6−6i6i0-303i3−3i3333−333i−3i000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000000000000000−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300000000

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