Finite Group Databasebeta

← Group #13180670

Character table — Group #13180670

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size112444444444444668899161616161616161616161616161616161818181818242424243636363654545454545472727272727272727272
order122333366666666446622333366666666666624444121212126666444444661212121212121212
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+i321111−1−i32−1+i321111−1−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+i321111−1−i32−1+i321111−1−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+i321111−1−i32−1+i321111−1−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+i321111−1−i32−1+i321111−1−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−i321111−1+i32−1−i321111−1+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−i321111−1+i32−1−i321111−1+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−i321111−1+i32−1−i321111−1+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−i321111−1+i32−1−i321111−1+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
χ1311-11111-1-1-1-111111-1-1-111111111-1-1-1-111-1-1-1-1-11-11-111-1-111111-11-11-1-1-11-11-11-11-1
χ1411-11111-1-1-1-111111-1-1-111111111-1-1-1-111-1-1-1-1-1-11-1111-1-111111-1-11-11-1-1-11-11-11-11
χ1511-11111-1-1-1-111111-1-1-1-1-1111111-1-1-1-111-1-1-1-11i−i−ii11-1-1-1-1-1-1-11i−i−ii11i−ii−i−ii−ii
χ1611-11111-1-1-1-111111-1-1-1-1-1111111-1-1-1-111-1-1-1-11−iii−i11-1-1-1-1-1-1-11−iii−i11−ii−iii−ii−i
χ1711-111−1−i32−1+i32-1-1-1-1−1−i32−1+i32111-11+i321−i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i32-11-11-111-1-1−1−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+i32-1-1-1-1−1−i32−1+i32111-11+i321−i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i32-1-11-1111-1-1−1−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+i32-1-1-1-1−1−i32−1+i32111-11+i321−i32-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i321i−i−ii11-1-11+i321+i321−i321−i32-11i−i−ii−1−i32−1+i32ζ11−ζ11ζ7−ζ7−ζ11ζ11−ζ7ζ7
χ2011-111−1−i32−1+i32-1-1-1-1−1−i32−1+i32111-11+i321−i32-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i321−iii−i11-1-11+i321+i321−i321−i32-11−iii−i−1−i32−1+i32−ζ11ζ11−ζ7ζ7ζ11−ζ11ζ7−ζ7
χ2111-111−1+i32−1−i32-1-1-1-1−1+i32−1−i32111-11−i321+i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i32-11-11-111-1-1−1+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−i32-1-1-1-1−1+i32−1−i32111-11−i321+i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i32-1-11-1111-1-1−1+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−i32-1-1-1-1−1+i32−1−i32111-11−i321+i32-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i321i−i−ii11-1-11−i321−i321+i321+i32-11i−i−ii−1+i32−1−i32ζ7−ζ7ζ11−ζ11−ζ7ζ7−ζ11ζ11
χ2411-111−1+i32−1−i32-1-1-1-1−1+i32−1−i32111-11−i321+i32-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i321−iii−i11-1-11−i321−i321+i321+i32-11−iii−i−1+i32−1−i32−ζ7ζ7−ζ11ζ11ζ7−ζ7ζ11−ζ11
χ25333330033330033-1-10033000000000000000033333-1-1-1-10000-1-1-1-1-1-10000000000
χ26333330033330033-1-1003300000000000000003-3-3-3-3-1-1-1-10000-1-111110000000000
χ27333330033330033-1-100-3-30000000000000000-33i3i−3i−3i-1-1-1-1000011−i−iii0000000000
χ28333330033330033-1-100-3-30000000000000000-3−3i−3i3i3i-1-1-1-1000011ii−i−i0000000000
χ2933-33300-3-3-3-30033-1100330000000000000000-33-33-3-1-1110000-11-11-110000000000
χ3033-33300-3-3-3-30033-1100330000000000000000-3-33-33-1-1110000-111-11-10000000000
χ3133-33300-3-3-3-30033-1100-3-3000000000000000033i−3i−3i3i-1-11100001-1−iii−i0000000000
χ3233-33300-3-3-3-30033-1100-3-300000000000000003−3i3i3i−3i-1-11100001-1i−i−ii0000000000
χ334441-24411-2-2441-24444001-21-21-211-2-21-211-2-2000001-21-200000000000000000000
χ344441-2−2−2i3−2+2i311-2-2−2−2i3−2+2i31-244−2−2i3−2+2i300−1−i321+i3−1+i321−i3−1−i321+i3−1−i32−1−i321+i31+i3−1+i321−i3−1+i32−1+i321−i31−i3000001-21-200000000000000000000
χ354441-2−2+2i3−2−2i311-2-2−2+2i3−2−2i31-244−2+2i3−2−2i300−1+i321−i3−1−i321+i3−1+i321−i3−1+i32−1+i321−i31−i3−1−i321+i3−1−i32−1−i321+i31+i3000001-21-200000000000000000000
χ36444-2144-2-21144-21444400-21-21-21-2-211-21-2-21100000-21-2100000000000000000000
χ37444-21−2−2i3−2+2i3-2-211−2−2i3−2+2i3-2144−2−2i3−2+2i3001+i3−1−i321−i3−1+i321+i3−1−i321+i31+i3−1−i32−1−i321−i3−1+i321−i31−i3−1+i32−1+i3200000-21-2100000000000000000000
χ38444-21−2+2i3−2−2i3-2-211−2+2i3−2−2i3-2144−2+2i3−2−2i3001−i3−1+i321+i3−1−i321−i3−1+i321−i31−i3−1+i32−1+i321+i3−1−i321+i31+i3−1−i32−1−i3200000-21-2100000000000000000000
χ3944-41-244-1-122441-24-4-4-4001-21-21-2-1-1221-2-1-122000001-2-1200000000000000000000
χ4044-41-2−2−2i3−2+2i3-1-122−2−2i3−2+2i31-24-42+2i32−2i300−1−i321+i3−1+i321−i3−1−i321+i31+i321+i32−1−i3−1−i3−1+i321−i31−i321−i32−1+i3−1+i3000001-2-1200000000000000000000
χ4144-41-2−2+2i3−2−2i3-1-122−2+2i3−2−2i31-24-42−2i32+2i300−1+i321−i3−1−i321+i3−1+i321−i31−i321−i32−1+i3−1+i3−1−i321+i31+i321+i32−1−i3−1−i3000001-2-1200000000000000000000
χ4244-4-214422-1-144-214-4-4-400-21-21-2122-1-1-2122-1-100000-212-100000000000000000000
χ4344-4-21−2−2i3−2+2i322-1-1−2−2i3−2+2i3-214-42+2i32−2i3001+i3−1−i321−i3−1+i321+i3−1−i32−1−i3−1−i31+i321+i321−i3−1+i32−1+i3−1+i31−i321−i3200000-212-100000000000000000000
χ4444-4-21−2+2i3−2−2i322-1-1−2+2i3−2−2i3-214-42−2i32+2i3001−i3−1+i321+i3−1−i321−i3−1+i32−1+i3−1+i31−i321−i321+i3−1−i32−1−i3−1−i31+i321+i3200000-212-100000000000000000000
χ454-4044-2-2000022-4-400004-4-2-2-2-22200002200000000000002-22-20000000000000000
χ464-4044-2-2000022-4-40000-44-2-2-2-2220000220000000000000-22-220000000000000000
χ474-40441+i31−i30000−1−i3−1+i3-4-400004-41+i31+i31−i31−i3−1−i3−1−i30000−1+i3−1+i30000000000000−1−i31+i3−1+i31−i30000000000000000
χ484-40441+i31−i30000−1−i3−1+i3-4-40000-441+i31+i31−i31−i3−1−i3−1−i30000−1+i3−1+i300000000000001+i3−1−i31−i3−1+i30000000000000000
χ494-40441−i31+i30000−1+i3−1−i3-4-400004-41−i31−i31+i31+i3−1+i3−1+i30000−1−i3−1−i30000000000000−1+i31−i3−1−i31+i30000000000000000
χ504-40441−i31+i30000−1+i3−1−i3-4-40000-441−i31−i31+i31+i3−1+i3−1+i30000−1−i3−1−i300000000000001−i3−1+i31+i3−1−i30000000000000000
χ518-802-4-4-46-60044-24000000-12-121-23-3001-23-30000000000000000000000000000000
χ528-802-4-4-4-660044-24000000-12-121-2-33001-2-330000000000000000000000000000000
χ538-802-42+2i32−2i36-600−2−2i3−2+2i3-240000001+i32−1−i31−i32−1+i3−1−i321+i3−3−3i323+3i3200−1+i321−i3−3+3i323−3i320000000000000000000000000000000
χ548-802-42+2i32−2i3-6600−2−2i3−2+2i3-240000001+i32−1−i31−i32−1+i3−1−i321+i33+3i32−3−3i3200−1+i321−i33−3i32−3+3i320000000000000000000000000000000
χ558-802-42−2i32+2i36-600−2+2i3−2−2i3-240000001−i32−1+i31+i32−1−i3−1+i321−i3−3+3i323−3i3200−1−i321+i3−3−3i323+3i320000000000000000000000000000000
χ568-802-42−2i32+2i3-6600−2+2i3−2−2i3-240000001−i32−1+i31+i32−1−i3−1+i321−i33−3i32−3+3i3200−1−i321+i33+3i32−3−3i320000000000000000000000000000000
χ578-80-42-4-4006-6444-20000002-12-1-21003-3-21003-300000000000000000000000000000
χ588-80-42-4-400-66444-20000002-12-1-2100-33-2100-3300000000000000000000000000000
χ598-80-422+2i32−2i3006-6−2−2i3−2+2i34-2000000−1−i31+i32−1+i31−i321+i3−1−i3200−3−3i323+3i321−i3−1+i3200−3+3i323−3i3200000000000000000000000000000
χ608-80-422+2i32−2i300-66−2−2i3−2+2i34-2000000−1−i31+i32−1+i31−i321+i3−1−i32003+3i32−3−3i321−i3−1+i32003−3i32−3+3i3200000000000000000000000000000
χ618-80-422−2i32+2i3006-6−2+2i3−2−2i34-2000000−1+i31−i32−1−i31+i321−i3−1+i3200−3+3i323−3i321+i3−1−i3200−3−3i323+3i3200000000000000000000000000000
χ628-80-422−2i32+2i300-66−2+2i3−2−2i34-2000000−1+i31−i32−1−i31+i321−i3−1+i32003−3i32−3+3i321+i3−1−i32003+3i32−3−3i3200000000000000000000000000000
χ631212123-60033-6-6003-6-4-40000000000000000000000000-12-1200000000000000000000
χ64121212-6300-6-63300-63-4-400000000000000000000000002-12-100000000000000000000
χ651212-123-600-3-366003-6-440000000000000000000000000-121-200000000000000000000
χ661212-12-630066-3-300-63-4400000000000000000000000002-1-2100000000000000000000

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