Finite Group Databasebeta

← Group #13180672

Character table — Group #13180672

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size112444444444444668899161616161616161616161616161616161818181818242424243636363654545454545472727272727272727272
order1243333666612121212241212443333666612121212121212122888866121212121212248888662424242424242424
χ1111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ31111111111111111111-1-11111111111111111-1ii−i−i1111-1-1-1-1-1-1ii−i−i-1-1iiii−i−i−i−i
χ41111111111111111111-1-11111111111111111-1−i−iii1111-1-1-1-1-1-1−i−iii-1-1−i−i−i−iiiii
χ511111−1−i32−1+i3211−1−i32−1+i32111111−1−i32−1+i3211−1−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+i32111111111−1−i32−1−i32−1+i32−1+i32111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ611111−1−i32−1+i3211−1−i32−1+i32111111−1−i32−1+i3211−1−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+i321-1-1-1-11111−1−i32−1−i32−1+i32−1+i3211-1-1-1-1−1−i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i32
χ711111−1−i32−1+i3211−1−i32−1+i32111111−1−i32−1+i32-1-1−1−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+i32−1+i32−1+i32-1ii−i−i11111+i321+i321−i321−i32-1-1ii−i−i1+i321−i32ζ11ζ11ζ7ζ7−ζ11−ζ11−ζ7−ζ7
χ811111−1−i32−1+i3211−1−i32−1+i32111111−1−i32−1+i32-1-1−1−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+i32−1+i32−1+i32-1−i−iii11111+i321+i321−i321−i32-1-1−i−iii1+i321−i32−ζ11−ζ11−ζ7−ζ7ζ11ζ11ζ7ζ7
χ911111−1+i32−1−i3211−1+i32−1−i32111111−1+i32−1−i3211−1+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−i32111111111−1+i32−1+i32−1−i32−1−i32111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ1011111−1+i32−1−i3211−1+i32−1−i32111111−1+i32−1−i3211−1+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−i321-1-1-1-11111−1+i32−1+i32−1−i32−1−i3211-1-1-1-1−1+i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i32
χ1111111−1+i32−1−i3211−1+i32−1−i32111111−1+i32−1−i32-1-1−1+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−i32−1−i32−1−i32-1ii−i−i11111−i321−i321+i321+i32-1-1ii−i−i1−i321+i32ζ7ζ7ζ11ζ11−ζ7−ζ7−ζ11−ζ11
χ1211111−1+i32−1−i3211−1+i32−1−i32111111−1+i32−1−i32-1-1−1+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−i32−1−i32−1−i32-1−i−iii11111−i321−i321+i321+i32-1-1−i−iii1−i321+i32−ζ7−ζ7−ζ11−ζ11ζ7ζ7ζ11ζ11
χ1311-111111111-1-1-1-1-11-1-11111111111-1-1-1-1-1-1-1-1-11-11-1-1-11111111-11-11-1-1-11-11-11-11-1
χ1411-111111111-1-1-1-1-11-1-11111111111-1-1-1-1-1-1-1-1-1-11-11-1-11111111-1-11-11-1-1-11-11-11-11
χ1511-111111111-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-11i−i−ii-1-111-1-1-1-1-11i−i−ii11i−ii−i−ii−ii
χ1611-111111111-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-11−iii−i-1-111-1-1-1-1-11−iii−i11−ii−iii−ii−i
χ1711-111−1−i32−1+i3211−1−i32−1+i32-1-1-1-1-111+i321−i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32-11-11-1-1-111−1−i32−1−i32−1+i32−1+i321-11-11-11+i321−i32−1−i321+i32−1+i321−i32−1−i321+i32−1+i321−i32
χ1811-111−1−i32−1+i3211−1−i32−1+i32-1-1-1-1-111+i321−i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32-1-11-11-1-111−1−i32−1−i32−1+i32−1+i321-1-11-111+i321−i321+i32−1−i321−i32−1+i321+i32−1−i321−i32−1+i32
χ1911-111−1−i32−1+i3211−1−i32−1+i32-1-1-1-1-111+i321−i32-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i321i−i−ii-1-1111+i321+i321−i321−i32-11i−i−ii−1−i32−1+i32ζ11−ζ11ζ7−ζ7−ζ11ζ11−ζ7ζ7
χ2011-111−1−i32−1+i3211−1−i32−1+i32-1-1-1-1-111+i321−i32-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i321−iii−i-1-1111+i321+i321−i321−i32-11−iii−i−1−i32−1+i32−ζ11ζ11−ζ7ζ7ζ11−ζ11ζ7−ζ7
χ2111-111−1+i32−1−i3211−1+i32−1−i32-1-1-1-1-111−i321+i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32-11-11-1-1-111−1+i32−1+i32−1−i32−1−i321-11-11-11−i321+i32−1+i321−i32−1−i321+i32−1+i321−i32−1−i321+i32
χ2211-111−1+i32−1−i3211−1+i32−1−i32-1-1-1-1-111−i321+i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32-1-11-11-1-111−1+i32−1+i32−1−i32−1−i321-1-11-111−i321+i321−i32−1+i321+i32−1−i321−i32−1+i321+i32−1−i32
χ2311-111−1+i32−1−i3211−1+i32−1−i32-1-1-1-1-111−i321+i32-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i321i−i−ii-1-1111−i321−i321+i321+i32-11i−i−ii−1+i32−1−i32ζ7−ζ7ζ11−ζ11−ζ7ζ7−ζ11ζ11
χ2411-111−1+i32−1−i3211−1+i32−1−i32-1-1-1-1-111−i321+i32-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i321−iii−i-1-1111−i321−i321+i321+i32-11−iii−i−1+i32−1−i32−ζ7ζ7−ζ11ζ11ζ7−ζ7ζ11−ζ11
χ25333330033003333-1-10033000000000000000033333-1-1-1-10000-1-1-1-1-1-10000000000
χ26333330033003333-1-1003300000000000000003-3-3-3-3-1-1-1-10000-1-111110000000000
χ27333330033003333-1-100-3-30000000000000000-33i3i−3i−3i-1-1-1-1000011−i−iii0000000000
χ28333330033003333-1-100-3-30000000000000000-3−3i−3i3i3i-1-1-1-1000011ii−i−i0000000000
χ2933-333003300-3-3-3-31-100330000000000000000-33-33-311-1-10000-11-11-110000000000
χ3033-333003300-3-3-3-31-100330000000000000000-3-33-3311-1-10000-111-11-10000000000
χ3133-333003300-3-3-3-31-100-3-3000000000000000033i−3i−3i3i11-1-100001-1−iii−i0000000000
χ3233-333003300-3-3-3-31-100-3-300000000000000003−3i3i3i−3i11-1-100001-1i−i−ii0000000000
χ334441-2441-24411-2-24444001-21-21-21-211-2-211-2-2000001-21-200000000000000000000
χ344441-2−2−2i3−2+2i31-2−2−2i3−2+2i311-2-244−2−2i3−2+2i300−1−i321+i3−1+i321−i3−1−i321+i3−1+i321−i3−1−i32−1−i321+i31+i3−1+i32−1+i321−i31−i3000001-21-200000000000000000000
χ354441-2−2+2i3−2−2i31-2−2+2i3−2−2i311-2-244−2+2i3−2−2i300−1+i321−i3−1−i321+i3−1+i321−i3−1−i321+i3−1+i32−1+i321−i31−i3−1−i32−1−i321+i31+i3000001-21-200000000000000000000
χ36444-2144-2144-2-211444400-21-21-21-21-2-211-2-21100000-21-2100000000000000000000
χ37444-21−2−2i3−2+2i3-21−2−2i3−2+2i3-2-21144−2−2i3−2+2i3001+i3−1−i321−i3−1+i321+i3−1−i321−i3−1+i321+i31+i3−1−i32−1−i321−i31−i3−1+i32−1+i3200000-21-2100000000000000000000
χ38444-21−2+2i3−2−2i3-21−2+2i3−2−2i3-2-21144−2+2i3−2−2i3001−i3−1+i321+i3−1−i321−i3−1+i321+i3−1−i321−i31−i3−1+i32−1+i321+i31+i3−1−i32−1−i3200000-21-2100000000000000000000
χ3944-41-2441-244-1-122-44-4-4001-21-21-21-2-1-122-1-12200000-121-200000000000000000000
χ4044-41-2−2−2i3−2+2i31-2−2−2i3−2+2i3-1-122-442+2i32−2i300−1−i321+i3−1+i321−i3−1−i321+i3−1+i321−i31+i321+i32−1−i3−1−i31−i321−i32−1+i3−1+i300000-121-200000000000000000000
χ4144-41-2−2+2i3−2−2i31-2−2+2i3−2−2i3-1-122-442−2i32+2i300−1+i321−i3−1−i321+i3−1+i321−i3−1−i321+i31−i321−i32−1+i3−1+i31+i321+i32−1−i3−1−i300000-121-200000000000000000000
χ4244-4-2144-214422-1-1-44-4-400-21-21-21-2122-1-122-1-1000002-1-2100000000000000000000
χ4344-4-21−2−2i3−2+2i3-21−2−2i3−2+2i322-1-1-442+2i32−2i3001+i3−1−i321−i3−1+i321+i3−1−i321−i3−1+i32−1−i3−1−i31+i321+i32−1+i3−1+i31−i321−i32000002-1-2100000000000000000000
χ4444-4-21−2+2i3−2−2i3-21−2+2i3−2−2i322-1-1-442−2i32+2i3001−i3−1+i321+i3−1−i321−i3−1+i321+i3−1−i32−1+i3−1+i31−i321−i32−1−i3−1−i31+i321+i32000002-1-2100000000000000000000
χ454-4044-2-2-4-422000000004i−4i-2-2-2-22222000000000000000002i−2i2i−2i0000000000000000
χ464-4044-2-2-4-42200000000−4i4i-2-2-2-2222200000000000000000−2i2i−2i2i0000000000000000
χ474-40441+i31−i3-4-4−1−i3−1+i3000000004i−4i1+i31+i31−i31−i3−1−i3−1−i3−1+i3−1+i3000000000000000002ζ11−2ζ112ζ7−2ζ70000000000000000
χ484-40441+i31−i3-4-4−1−i3−1+i300000000−4i4i1+i31+i31−i31−i3−1−i3−1−i3−1+i3−1+i300000000000000000−2ζ112ζ11−2ζ72ζ70000000000000000
χ494-40441−i31+i3-4-4−1+i3−1−i3000000004i−4i1−i31−i31+i31+i3−1+i3−1+i3−1−i3−1−i3000000000000000002ζ7−2ζ72ζ11−2ζ110000000000000000
χ504-40441−i31+i3-4-4−1+i3−1−i300000000−4i4i1−i31−i31+i31+i3−1+i3−1+i3−1−i3−1−i300000000000000000−2ζ72ζ7−2ζ112ζ110000000000000000
χ518-802-4-4-4-24446i−6i00000000-12-121-21-23i−3i003i−3i0000000000000000000000000000000
χ528-802-4-4-4-2444−6i6i00000000-12-121-21-2−3i3i00−3i3i0000000000000000000000000000000
χ538-802-42+2i32−2i3-24−2−2i3−2+2i36i−6i000000001+i32−1−i31−i32−1+i3−1−i321+i3−1+i321−i33ζ11−3ζ11003ζ7−3ζ70000000000000000000000000000000
χ548-802-42+2i32−2i3-24−2−2i3−2+2i3−6i6i000000001+i32−1−i31−i32−1+i3−1−i321+i3−1+i321−i3−3ζ113ζ1100−3ζ73ζ70000000000000000000000000000000
χ558-802-42−2i32+2i3-24−2+2i3−2−2i36i−6i000000001−i32−1+i31+i32−1−i3−1+i321−i3−1−i321+i33ζ7−3ζ7003ζ11−3ζ110000000000000000000000000000000
χ568-802-42−2i32+2i3-24−2+2i3−2−2i3−6i6i000000001−i32−1+i31+i32−1−i3−1+i321−i3−1−i321+i3−3ζ73ζ700−3ζ113ζ110000000000000000000000000000000
χ578-80-42-4-44-244006i−6i0000002-12-1-21-21003i−3i003i−3i00000000000000000000000000000
χ588-80-42-4-44-24400−6i6i0000002-12-1-21-2100−3i3i00−3i3i00000000000000000000000000000
χ598-80-422+2i32−2i34-2−2−2i3−2+2i3006i−6i000000−1−i31+i32−1+i31−i321+i3−1−i321−i3−1+i32003ζ11−3ζ11003ζ7−3ζ700000000000000000000000000000
χ608-80-422+2i32−2i34-2−2−2i3−2+2i300−6i6i000000−1−i31+i32−1+i31−i321+i3−1−i321−i3−1+i3200−3ζ113ζ1100−3ζ73ζ700000000000000000000000000000
χ618-80-422−2i32+2i34-2−2+2i3−2−2i3006i−6i000000−1+i31−i32−1−i31+i321−i3−1+i321+i3−1−i32003ζ7−3ζ7003ζ11−3ζ1100000000000000000000000000000
χ628-80-422−2i32+2i34-2−2+2i3−2−2i300−6i6i000000−1+i31−i32−1−i31+i321−i3−1+i321+i3−1−i3200−3ζ73ζ700−3ζ113ζ1100000000000000000000000000000
χ631212123-6003-60033-6-6-4-40000000000000000000000000-12-1200000000000000000000
χ64121212-6300-6300-6-633-4-400000000000000000000000002-12-100000000000000000000
χ651212-123-6003-600-3-3664-400000000000000000000000001-2-1200000000000000000000
χ661212-12-6300-630066-3-34-40000000000000000000000000-212-100000000000000000000

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