Finite Group Databasebeta

← Group #13147049

Character table — Group #13147049

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size11111122233333344466666666666121212121212121212121212121212242424242424363636363636363636363636484848484848484848727272727272
order1233664121222666626634666666612122666666666612121212333666888824242424242424246666661212124412121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1
χ3111111111111111-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1111-1-1-1-1-1-1
χ4111111111111111-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111
χ522222222222222222222222222222222222222222222-1-1-1-1-1-1000000000000-1-1-1-1-1-1-1-1-1000000
χ6222222222222222222-12-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-1-12-1-12-1-100000000000022-1-1-1-12-1-1000000
χ7222222222222222222-12-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-1-1-12-1-12-1000000000000-1-122-1-1-12-1000000
χ8222222222222222222-12-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-12000000000000-1-1-1-122-1-12000000
χ9222222222222222-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-22222-1-1-1-1-1-1000000000000111111-1-1-1000000
χ10222222222222222-2-2-2-12-1-1-1-1-1-1-122-2-2-211111111-1-1-1-12-1-12-1-1000000000000-2-211112-1-1000000
χ11222222222222222-2-2-2-12-1-1-1-1-1-1-122-2-2-211111111-1-1-1-1-12-1-12-100000000000011-2-211-12-1000000
χ12222222222222222-2-2-2-12-1-1-1-1-1-1-122-2-2-211111111-1-1-1-1-1-12-1-120000000000001111-2-2-1-12000000
χ13222222-2-2-22222220002-22222222-2-200000000000-2-2-2-2222222000000000000000000-2-2-2000000
χ14222222-2-2-22222220002-22222222-2-200000000000-2-2-2-2-1-1-1-1-1-1000000000000−i3i3−i3i3−i3i3111000000
χ15222222-2-2-22222220002-22222222-2-200000000000-2-2-2-2-1-1-1-1-1-1000000000000i3−i3i3−i3i3−i3111000000
χ16222222-2-2-2222222000-1-2-1-1-1-1-1-1-1-2-2000−i3−i3−i3−i3i3i3i3i311112-1-12-1-100000000000000−i3i3i3−i3-211000000
χ17222222-2-2-2222222000-1-2-1-1-1-1-1-1-1-2-2000−i3−i3−i3−i3i3i3i3i31111-12-1-12-1000000000000i3−i300−i3i31-21000000
χ18222222-2-2-2222222000-1-2-1-1-1-1-1-1-1-2-2000−i3−i3−i3−i3i3i3i3i31111-1-12-1-12000000000000−i3i3i3−i30011-2000000
χ19222222-2-2-2222222000-1-2-1-1-1-1-1-1-1-2-2000i3i3i3i3−i3−i3−i3−i311112-1-12-1-100000000000000i3−i3−i3i3-211000000
χ20222222-2-2-2222222000-1-2-1-1-1-1-1-1-1-2-2000i3i3i3i3−i3−i3−i3−i31111-12-1-12-1000000000000−i3i300i3−i31-21000000
χ21222222-2-2-2222222000-1-2-1-1-1-1-1-1-1-2-2000i3i3i3i3−i3−i3−i3−i31111-1-12-1-12000000000000i3−i3−i3i30011-2000000
χ222-222-2-20002-222-2-200020222-2-2-2-200000000000000000222-2-2-2−i2i2−i2i2−i2−i2i2i2−i2−i2i2i2000000000000000
χ232-222-2-20002-222-2-200020222-2-2-2-200000000000000000222-2-2-2i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2000000000000000
χ24333333333-1-1-1-1-1-13333-1-1-1-1-1-1-13-1-1-1-1-13-1-1-13-1-1-13-1-1-100000011-1-11111-1-1-1-10000000001-111-1-1
χ25333333333-1-1-1-1-1-13333-1-1-1-1-1-1-13-1-1-1-1-13-1-1-13-1-1-13-1-1-1000000-1-111-1-1-1-11111000000000-11-1-111
χ26333333333-1-1-1-1-1-1-3-3-33-1-1-1-1-1-1-13-1-1111-3111-31113-1-1-100000011-1-11111-1-1-1-1000000000-11-1-111
χ27333333333-1-1-1-1-1-1-3-3-33-1-1-1-1-1-1-13-1-1111-3111-31113-1-1-1000000-1-111-1-1-1-111110000000001-111-1-1
χ2833−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32030000000−3−3i32−3+3i323−3−3i32−3+3i320000000000000000001111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3200000000011−1−i32−1+i32−1−i32−1+i32
χ2933−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32030000000−3−3i32−3+3i323−3−3i32−3+3i32000000000000000000-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i32000000000-1-11+i321−i321+i321−i32
χ3033−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32-33+3i323−3i32030000000−3−3i32−3+3i32-33+3i323−3i320000000000000000001111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32000000000-1-11+i321−i321+i321−i32
χ3133−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32-33+3i323−3i32030000000−3−3i32−3+3i32-33+3i323−3i32000000000000000000-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i3200000000011−1−i32−1+i32−1−i32−1+i32
χ3233−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32-1-11+i321−i321+i321−i323−3−3i32−3+3i320-12−1−i3−1+i32−1−i3−1+i301+i321−i32-11+i321−i3202−1−i3−1+i302−1−i3−1+i302−1−i3−1+i300000011-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i320000000001-1−1−i32−1+i321+i321−i32
χ3333−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32-1-11+i321−i321+i321−i323−3−3i32−3+3i320-12−1−i3−1+i32−1−i3−1+i301+i321−i32-11+i321−i3202−1−i3−1+i302−1−i3−1+i302−1−i3−1+i3000000-1-1111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32000000000-111+i321−i32−1−i32−1+i32
χ3433−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32-1-11+i321−i321+i321−i32-33+3i323−3i320-12−1−i3−1+i32−1−i3−1+i301+i321−i321−1−i32−1+i320-21+i31−i30-21+i31−i302−1−i3−1+i300000011-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32000000000-111+i321−i32−1−i32−1+i32
χ3533−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32-1-11+i321−i321+i321−i32-33+3i323−3i320-12−1−i3−1+i32−1−i3−1+i301+i321−i321−1−i32−1+i320-21+i31−i30-21+i31−i302−1−i3−1+i3000000-1-1111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i320000000001-1−1−i32−1+i321+i321−i32
χ3633−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32030000000−3+3i32−3−3i323−3+3i32−3−3i320000000000000000001111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3200000000011−1+i32−1−i32−1+i32−1−i32
χ3733−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32030000000−3+3i32−3−3i323−3+3i32−3−3i32000000000000000000-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i32000000000-1-11−i321+i321−i321+i32
χ3833−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32-33−3i323+3i32030000000−3+3i32−3−3i32-33−3i323+3i320000000000000000001111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32000000000-1-11−i321+i321−i321+i32
χ3933−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32-33−3i323+3i32030000000−3+3i32−3−3i32-33−3i323+3i32000000000000000000-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i3200000000011−1+i32−1−i32−1+i32−1−i32
χ4033−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32-1-11−i321+i321−i321+i323−3+3i32−3−3i320-12−1+i3−1−i32−1+i3−1−i301−i321+i32-11−i321+i3202−1+i3−1−i302−1+i3−1−i302−1+i3−1−i300000011-1-1−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i320000000001-1−1+i32−1−i321−i321+i32
χ4133−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32-1-11−i321+i321−i321+i323−3+3i32−3−3i320-12−1+i3−1−i32−1+i3−1−i301−i321+i32-11−i321+i3202−1+i3−1−i302−1+i3−1−i302−1+i3−1−i3000000-1-1111−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i32000000000-111−i321+i32−1+i32−1−i32
χ4233−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32-1-11−i321+i321−i321+i32-33−3i323+3i320-12−1+i3−1−i32−1+i3−1−i301−i321+i321−1+i32−1−i320-21−i31+i30-21−i31+i302−1+i3−1−i300000011-1-1−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32000000000-111−i321+i32−1+i32−1−i32
χ4333−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32-1-11−i321+i321−i321+i32-33−3i323+3i320-12−1+i3−1−i32−1+i3−1−i301−i321+i321−1+i32−1−i320-21−i31+i30-21−i31+i302−1+i3−1−i3000000-1-1111−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i320000000001-1−1+i32−1−i321−i321+i32
χ444-444-4-40004-444-4-400040444-4-4-4-400000000000000000-2-2-2222000000000000000000000000000
χ454-444-4-40004-444-4-4000-20-2-2-22222000000000000000004-2-2-422000000000000000000000000000
χ464-444-4-40004-444-4-4000-20-2-2-2222200000000000000000-24-22-42000000000000000000000000000
χ474-444-4-40004-444-4-4000-20-2-2-2222200000000000000000-2-2422-4000000000000000000000000000
χ48666666666-2-2-2-2-2-2666-3-2111111-3-2-2-2-2-2-3111-3111-3111000000000000000000000000000000000
χ49666666666-2-2-2-2-2-2-6-6-6-3-2111111-3-2-22223-1-1-13-1-1-1-3111000000000000000000000000000000000
χ50666666-6-6-6-2-2-2-2-2-200062-2-2-2-2-2-262200000000000-6222000000000000000000000000000000000
χ51666666-6-6-6-2-2-2-2-2-2000-32111111-322000−3i3i3i3i33i3−i3−i3−i33-1-1-1000000000000000000000000000000000
χ52666666-6-6-6-2-2-2-2-2-2000-32111111-3220003i3−i3−i3−i3−3i3i3i3i33-1-1-1000000000000000000000000000000000
χ5366−3−3i3−3+3i3−3−3i3−3+3i36−3−3i3−3+3i3-2-21+i31−i31+i31−i36−3−3i3−3+3i30-2-21+i31−i3-21+i31−i301+i31−i3-21+i31−i30-21+i31−i30-21+i31−i30-21+i31−i3000000000000000000000000000000000
χ5466−3−3i3−3+3i3−3−3i3−3+3i36−3−3i3−3+3i3-2-21+i31−i31+i31−i3-63+3i33−3i30-2-21+i31−i3-21+i31−i301+i31−i32−1−i3−1+i302−1−i3−1+i302−1−i3−1+i30-21+i31−i3000000000000000000000000000000000
χ5566−3−3i3−3+3i3−3−3i3−3+3i3-63+3i33−3i366−3−3i3−3+3i3−3−3i3−3+3i30000-600000003+3i33−3i3000000000000000000000000000000000000000000000000
χ5666−3−3i3−3+3i3−3−3i3−3+3i3-63+3i33−3i3-2-21+i31−i31+i31−i3000024−2−2i3−2+2i34−2−2i3−2+2i30−1−i3−1+i3000000000000-42+2i32−2i3000000000000000000000000000000000
χ5766−3−3i3−3+3i3−3−3i3−3+3i3-63+3i33−3i3-2-21+i31−i31+i31−i300002-21+i31−i3-21+i31−i30−1−i3−1+i30000−2i3−3+i33+i302i33−i3−3−i302−1−i3−1+i3000000000000000000000000000000000
χ5866−3−3i3−3+3i3−3−3i3−3+3i3-63+3i33−3i3-2-21+i31−i31+i31−i300002-21+i31−i3-21+i31−i30−1−i3−1+i300002i33−i3−3−i30−2i3−3+i33+i302−1−i3−1+i3000000000000000000000000000000000
χ5966−3+3i3−3−3i3−3+3i3−3−3i36−3+3i3−3−3i3-2-21−i31+i31−i31+i36−3+3i3−3−3i30-2-21−i31+i3-21−i31+i301−i31+i3-21−i31+i30-21−i31+i30-21−i31+i30-21−i31+i3000000000000000000000000000000000
χ6066−3+3i3−3−3i3−3+3i3−3−3i36−3+3i3−3−3i3-2-21−i31+i31−i31+i3-63−3i33+3i30-2-21−i31+i3-21−i31+i301−i31+i32−1+i3−1−i302−1+i3−1−i302−1+i3−1−i30-21−i31+i3000000000000000000000000000000000
χ6166−3+3i3−3−3i3−3+3i3−3−3i3-63−3i33+3i366−3+3i3−3−3i3−3+3i3−3−3i30000-600000003−3i33+3i3000000000000000000000000000000000000000000000000
χ6266−3+3i3−3−3i3−3+3i3−3−3i3-63−3i33+3i3-2-21−i31+i31−i31+i3000024−2+2i3−2−2i34−2+2i3−2−2i30−1+i3−1−i3000000000000-42−2i32+2i3000000000000000000000000000000000
χ6366−3+3i3−3−3i3−3+3i3−3−3i3-63−3i33+3i3-2-21−i31+i31−i31+i300002-21−i31+i3-21−i31+i30−1+i3−1−i30000−2i33+i3−3+i302i3−3−i33−i302−1+i3−1−i3000000000000000000000000000000000
χ6466−3+3i3−3−3i3−3+3i3−3−3i3-63−3i33+3i3-2-21−i31+i31−i31+i300002-21−i31+i3-21−i31+i30−1+i3−1−i300002i3−3−i33−i30−2i33+i3−3+i302−1+i3−1−i3000000000000000000000000000000000
χ656-666-6-6000-22-2-22200060-2-2-2222-600000000000000000000000−i2i2i2−i2−i2−i2i2i2i2i2−i2−i2000000000000000
χ666-666-6-6000-22-2-22200060-2-2-2222-600000000000000000000000i2−i2−i2i2i2i2−i2−i2−i2−i2i2i2000000000000000
χ676-6−3−3i3−3+3i33+3i33−3i30006-6−3−3i3−3+3i33+3i33−3i300000000000000000000000000000000000−i2i2−i2i2ζ7+ζ13ζ5+ζ23−ζ7−ζ13−ζ5−ζ23ζ7+ζ13ζ5+ζ23−ζ7−ζ13−ζ5−ζ23000000000000000
χ686-6−3−3i3−3+3i33+3i33−3i30006-6−3−3i3−3+3i33+3i33−3i300000000000000000000000000000000000i2−i2i2−i2−ζ7−ζ13−ζ5−ζ23ζ7+ζ13ζ5+ζ23−ζ7−ζ13−ζ5−ζ23ζ7+ζ13ζ5+ζ23000000000000000
χ696-6−3−3i3−3+3i33+3i33−3i3000-221+i31−i3−1−i3−1+i3000004−2−2i3−2+2i3-42+2i32−2i3000000000000000000000000−i2i2i2−i2ζ7+ζ13ζ5+ζ23−ζ7−ζ13−ζ5−ζ23−ζ7−ζ13−ζ5−ζ23ζ7+ζ13ζ5+ζ23000000000000000
χ706-6−3−3i3−3+3i33+3i33−3i3000-221+i31−i3−1−i3−1+i3000004−2−2i3−2+2i3-42+2i32−2i3000000000000000000000000i2−i2−i2i2−ζ7−ζ13−ζ5−ζ23ζ7+ζ13ζ5+ζ23ζ7+ζ13ζ5+ζ23−ζ7−ζ13−ζ5−ζ23000000000000000
χ716-6−3+3i3−3−3i33−3i33+3i30006-6−3+3i3−3−3i33−3i33+3i300000000000000000000000000000000000−i2i2−i2i2ζ5+ζ23ζ7+ζ13−ζ5−ζ23−ζ7−ζ13ζ5+ζ23ζ7+ζ13−ζ5−ζ23−ζ7−ζ13000000000000000
χ726-6−3+3i3−3−3i33−3i33+3i30006-6−3+3i3−3−3i33−3i33+3i300000000000000000000000000000000000i2−i2i2−i2−ζ5−ζ23−ζ7−ζ13ζ5+ζ23ζ7+ζ13−ζ5−ζ23−ζ7−ζ13ζ5+ζ23ζ7+ζ13000000000000000
χ736-6−3+3i3−3−3i33−3i33+3i3000-221−i31+i3−1+i3−1−i3000004−2+2i3−2−2i3-42−2i32+2i3000000000000000000000000−i2i2i2−i2ζ5+ζ23ζ7+ζ13−ζ5−ζ23−ζ7−ζ13−ζ5−ζ23−ζ7−ζ13ζ5+ζ23ζ7+ζ13000000000000000
χ746-6−3+3i3−3−3i33−3i33+3i3000-221−i31+i3−1+i3−1−i3000004−2+2i3−2−2i3-42−2i32+2i3000000000000000000000000i2−i2−i2i2−ζ5−ζ23−ζ7−ζ13ζ5+ζ23ζ7+ζ13ζ5+ζ23ζ7+ζ13−ζ5−ζ23−ζ7−ζ13000000000000000
χ7512-121212-12-12000-44-4-444000-60222-2-2-2600000000000000000000000000000000000000000000000000
χ7612-12−6−6i3−6+6i36+6i36−6i3000-442+2i32−2i3−2−2i3−2+2i300000-42+2i32−2i34−2−2i3−2+2i3000000000000000000000000000000000000000000000000000
χ7712-12−6+6i3−6−6i36−6i36+6i3000-442−2i32+2i3−2+2i3−2−2i300000-42−2i32+2i34−2+2i3−2−2i3000000000000000000000000000000000000000000000000000

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