Finite Group Databasebeta

← Group #13180664

Character table — Group #13180664

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11244444444991818181818336121212121212121227275454545454448161616161616161636367272727272448161616161616161636367272727272
order124336612121212442888822466661212121244288883612336612121212121262424242436123366121212121212624242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111-1-1-1-111111111111111-1-1-1-111111111111111-1-1-1-111111111111111-1-1-1-1
χ311111111111-1-1-1ii−i−i11111111111-1-1-1ii−i−i11111111111-1-1-1ii−i−i11111111111-1-1-1ii−i−i
χ411111111111-1-1-1−i−iii11111111111-1-1-1−i−iii11111111111-1-1-1−i−iii11111111111-1-1-1−i−iii
χ511-11111-1-1-1-111-11-11-111-11111-1-1-1-111-11-11-111-11111-1-1-1-111-11-11-111-11111-1-1-1-111-11-11-1
χ611-11111-1-1-1-111-1-11-1111-11111-1-1-1-111-1-11-1111-11111-1-1-1-111-1-11-1111-11111-1-1-1-111-1-11-11
χ711-11111-1-1-1-1-1-11i−i−ii11-11111-1-1-1-1-1-11i−i−ii11-11111-1-1-1-1-1-11i−i−ii11-11111-1-1-1-1-1-11i−i−ii
χ811-11111-1-1-1-1-1-11−iii−i11-11111-1-1-1-1-1-11−iii−i11-11111-1-1-1-1-1-11−iii−i11-11111-1-1-1-1-1-11−iii−i
χ92-2022-2-200002i−2i000002-2022-2-200002i−2i000002-2022-2-200002i−2i000002-2022-2-200002i−2i00000
χ102-2022-2-20000−2i2i000002-2022-2-20000−2i2i000002-2022-2-20000−2i2i000002-2022-2-20000−2i2i00000
χ114441-21-211-2-200000004441-21-211-2-200000004441-21-211-2-200000004441-21-211-2-20000000
χ12444-21-21-2-2110000000444-21-21-2-2110000000444-21-21-2-2110000000444-21-21-2-2110000000
χ1344-41-21-2-1-122000000044-41-21-2-1-122000000044-41-21-2-1-122000000044-41-21-2-1-1220000000
χ1444-4-21-2122-1-1000000044-4-21-2122-1-1000000044-4-21-2122-1-1000000044-4-21-2122-1-10000000
χ154-401-2-123i−3i0000000004-401-2-123i−3i0000000004-401-2-123i−3i0000000004-401-2-123i−3i000000000
χ164-401-2-12−3i3i0000000004-401-2-12−3i3i0000000004-401-2-12−3i3i0000000004-401-2-12−3i3i000000000
χ174-40-212-1003i−3i00000004-40-212-1003i−3i00000004-40-212-1003i−3i00000004-40-212-1003i−3i0000000
χ184-40-212-100−3i3i00000004-40-212-100−3i3i00000004-40-212-100−3i3i00000004-40-212-100−3i3i0000000
χ19111111111111111111111111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ2011111111111111-1-1-1-111111111111111-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32
χ2111111111111-1-1-1ii−i−i11111111111-1-1-1ii−i−i−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32ζ7ζ7−ζ7−ζ7−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32ζ11ζ11−ζ11−ζ11
χ2211111111111-1-1-1−i−iii11111111111-1-1-1−i−iii−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−ζ7−ζ7ζ7ζ7−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−ζ11−ζ11ζ11ζ11
χ2311-11111-1-1-1-111-11-11-111-11111-1-1-1-111-11-11-1−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i32−1+i321−i32−1+i321−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i32−1−i321+i32−1−i321+i32
χ2411-11111-1-1-1-111-1-11-1111-11111-1-1-1-111-1-11-11−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−i32−1+i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i32
χ2511-11111-1-1-1-1-1-11i−i−ii11-11111-1-1-1-1-1-11i−i−ii−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32ζ7−ζ7−ζ7ζ7−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32ζ11−ζ11−ζ11ζ11
χ2611-11111-1-1-1-1-1-11−iii−i11-11111-1-1-1-1-1-11−iii−i−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−ζ7ζ7ζ7−ζ7−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−ζ11ζ11ζ11−ζ11
χ272-2022-2-200002i−2i000002-2022-2-200002i−2i00000−1+i31−i30−1+i3−1+i31−i31−i300002ζ7−2ζ700000−1−i31+i30−1−i3−1−i31+i31+i300002ζ11−2ζ1100000
χ282-2022-2-20000−2i2i000002-2022-2-20000−2i2i00000−1+i31−i30−1+i3−1+i31−i31−i30000−2ζ72ζ700000−1−i31+i30−1−i3−1−i31+i31+i30000−2ζ112ζ1100000
χ294441-21-211-2-200000004441-21-211-2-20000000−2+2i3−2+2i3−2+2i3−1+i321−i3−1+i321−i3−1+i32−1+i321−i31−i30000000−2−2i3−2−2i3−2−2i3−1−i321+i3−1−i321+i3−1−i32−1−i321+i31+i30000000
χ30444-21-21-2-2110000000444-21-21-2-2110000000−2+2i3−2+2i3−2+2i31−i3−1+i321−i3−1+i321−i31−i3−1+i32−1+i320000000−2−2i3−2−2i3−2−2i31+i3−1−i321+i3−1−i321+i31+i3−1−i32−1−i320000000
χ3144-41-21-2-1-122000000044-41-21-2-1-1220000000−2+2i3−2+2i32−2i3−1+i321−i3−1+i321−i31−i321−i32−1+i3−1+i30000000−2−2i3−2−2i32+2i3−1−i321+i3−1−i321+i31+i321+i32−1−i3−1−i30000000
χ3244-4-21-2122-1-1000000044-4-21-2122-1-10000000−2+2i3−2+2i32−2i31−i3−1+i321−i3−1+i32−1+i3−1+i31−i321−i320000000−2−2i3−2−2i32+2i31+i3−1−i321+i3−1−i32−1−i3−1−i31+i321+i320000000
χ334-401-2-123i−3i0000000004-401-2-123i−3i000000000−2+2i32−2i30−1+i321−i31−i32−1+i33ζ7−3ζ7000000000−2−2i32+2i30−1−i321+i31+i32−1−i33ζ11−3ζ11000000000
χ344-401-2-12−3i3i0000000004-401-2-12−3i3i000000000−2+2i32−2i30−1+i321−i31−i32−1+i3−3ζ73ζ7000000000−2−2i32+2i30−1−i321+i31+i32−1−i3−3ζ113ζ11000000000
χ354-40-212-1003i−3i00000004-40-212-1003i−3i0000000−2+2i32−2i301−i3−1+i32−1+i31−i32003ζ7−3ζ70000000−2−2i32+2i301+i3−1−i32−1−i31+i32003ζ11−3ζ110000000
χ364-40-212-100−3i3i00000004-40-212-100−3i3i0000000−2+2i32−2i301−i3−1+i32−1+i31−i3200−3ζ73ζ70000000−2−2i32+2i301+i3−1−i32−1−i31+i3200−3ζ113ζ110000000
χ37111111111111111111111111111111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ3811111111111111-1-1-1-111111111111111-1-1-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32
χ3911111111111-1-1-1ii−i−i11111111111-1-1-1ii−i−i−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32ζ11ζ11−ζ11−ζ11−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32ζ7ζ7−ζ7−ζ7
χ4011111111111-1-1-1−i−iii11111111111-1-1-1−i−iii−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−ζ11−ζ11ζ11ζ11−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−ζ7−ζ7ζ7ζ7
χ4111-11111-1-1-1-111-11-11-111-11111-1-1-1-111-11-11-1−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i32−1−i321+i32−1−i321+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i32−1+i321−i32−1+i321−i32
χ4211-11111-1-1-1-111-1-11-1111-11111-1-1-1-111-1-11-11−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−i32−1+i32
χ4311-11111-1-1-1-1-1-11i−i−ii11-11111-1-1-1-1-1-11i−i−ii−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32ζ11−ζ11−ζ11ζ11−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32ζ7−ζ7−ζ7ζ7
χ4411-11111-1-1-1-1-1-11−iii−i11-11111-1-1-1-1-1-11−iii−i−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−ζ11ζ11ζ11−ζ11−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−ζ7ζ7ζ7−ζ7
χ452-2022-2-200002i−2i000002-2022-2-200002i−2i00000−1−i31+i30−1−i3−1−i31+i31+i300002ζ11−2ζ1100000−1+i31−i30−1+i3−1+i31−i31−i300002ζ7−2ζ700000
χ462-2022-2-20000−2i2i000002-2022-2-20000−2i2i00000−1−i31+i30−1−i3−1−i31+i31+i30000−2ζ112ζ1100000−1+i31−i30−1+i3−1+i31−i31−i30000−2ζ72ζ700000
χ474441-21-211-2-200000004441-21-211-2-20000000−2−2i3−2−2i3−2−2i3−1−i321+i3−1−i321+i3−1−i32−1−i321+i31+i30000000−2+2i3−2+2i3−2+2i3−1+i321−i3−1+i321−i3−1+i32−1+i321−i31−i30000000
χ48444-21-21-2-2110000000444-21-21-2-2110000000−2−2i3−2−2i3−2−2i31+i3−1−i321+i3−1−i321+i31+i3−1−i32−1−i320000000−2+2i3−2+2i3−2+2i31−i3−1+i321−i3−1+i321−i31−i3−1+i32−1+i320000000
χ4944-41-21-2-1-122000000044-41-21-2-1-1220000000−2−2i3−2−2i32+2i3−1−i321+i3−1−i321+i31+i321+i32−1−i3−1−i30000000−2+2i3−2+2i32−2i3−1+i321−i3−1+i321−i31−i321−i32−1+i3−1+i30000000
χ5044-4-21-2122-1-1000000044-4-21-2122-1-10000000−2−2i3−2−2i32+2i31+i3−1−i321+i3−1−i32−1−i3−1−i31+i321+i320000000−2+2i3−2+2i32−2i31−i3−1+i321−i3−1+i32−1+i3−1+i31−i321−i320000000
χ514-401-2-123i−3i0000000004-401-2-123i−3i000000000−2−2i32+2i30−1−i321+i31+i32−1−i33ζ11−3ζ11000000000−2+2i32−2i30−1+i321−i31−i32−1+i33ζ7−3ζ7000000000
χ524-401-2-12−3i3i0000000004-401-2-12−3i3i000000000−2−2i32+2i30−1−i321+i31+i32−1−i3−3ζ113ζ11000000000−2+2i32−2i30−1+i321−i31−i32−1+i3−3ζ73ζ7000000000
χ534-40-212-1003i−3i00000004-40-212-1003i−3i0000000−2−2i32+2i301+i3−1−i32−1−i31+i32003ζ11−3ζ110000000−2+2i32−2i301−i3−1+i32−1+i31−i32003ζ7−3ζ70000000
χ544-40-212-100−3i3i00000004-40-212-100−3i3i0000000−2−2i32+2i301+i3−1−i32−1−i31+i3200−3ζ113ζ110000000−2+2i32−2i301−i3−1+i32−1+i31−i3200−3ζ73ζ70000000
χ55333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ5633333333333333-3-3-3-3-1-1-1-1-1-1-1-1-1-1-1-1-1-11111000000000000000000000000000000000000
χ5733333333333-3-3-33i3i−3i−3i-1-1-1-1-1-1-1-1-1-1-1111−i−iii000000000000000000000000000000000000
χ5833333333333-3-3-3−3i−3i3i3i-1-1-1-1-1-1-1-1-1-1-1111ii−i−i000000000000000000000000000000000000
χ5933-33333-3-3-3-333-33-33-3-1-11-1-1-1-11111-1-11-11-11000000000000000000000000000000000000
χ6033-33333-3-3-3-333-3-33-33-1-11-1-1-1-11111-1-111-11-1000000000000000000000000000000000000
χ6133-33333-3-3-3-3-3-333i−3i−3i3i-1-11-1-1-1-1111111-1−iii−i000000000000000000000000000000000000
χ6233-33333-3-3-3-3-3-33−3i3i3i−3i-1-11-1-1-1-1111111-1i−i−ii000000000000000000000000000000000000
χ636-6066-6-600006i−6i00000-220-2-2220000−2i2i00000000000000000000000000000000000000000
χ646-6066-6-60000−6i6i00000-220-2-22200002i−2i00000000000000000000000000000000000000000
χ651212123-63-633-6-60000000-4-4-4-12-12-1-1220000000000000000000000000000000000000000000
χ66121212-63-63-6-6330000000-4-4-42-12-122-1-10000000000000000000000000000000000000000000
χ671212-123-63-6-3-3660000000-4-44-12-1211-2-20000000000000000000000000000000000000000000
χ681212-12-63-6366-3-30000000-4-442-12-1-2-2110000000000000000000000000000000000000000000
χ6912-1203-6-369i−9i000000000-440-121-2−3i3i000000000000000000000000000000000000000000000
χ7012-1203-6-36−9i9i000000000-440-121-23i−3i000000000000000000000000000000000000000000000
χ7112-120-636-3009i−9i0000000-4402-1-2100−3i3i0000000000000000000000000000000000000000000
χ7212-120-636-300−9i9i0000000-4402-1-21003i−3i0000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.