Finite Group Databasebeta

← Group #13147082

Character table — Group #13147082

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111122244466666666121212121212121212121212121212121212242424242424363636363636484848484848484848727272727272727272
order12336641212266234666121246666612121212121212121212121233366644121212126666661212122668824242424
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1
χ3111111111-1-1-111111111-1111-1-1-1-11111-1-1-1-1-1-1111111111111-1-1-1-1-1-1111-1-1-11-111-1-1
χ4111111111-1-1-111111111-1111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-11-1-111
χ522222222222222222222222222222222222222-1-1-1-1-1-1000000-1-1-1-1-1-1-1-1-1000000000
χ62222222222222-1222-1222-1-1-1-1-122-1-1-1-1-1-1-1-1-1-12-1-12-1-100000022-1-1-1-12-1-1000000000
χ72222222222222-1222-1222-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-12-1-12-1000000-1-122-1-1-12-1000000000
χ82222222222222-1222-1222-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-12-1-12000000-1-1-1-122-1-12000000000
χ9222222222-2-2-222222222-2222-2-2-2-22222-2-2-2-2-2-2-1-1-1-1-1-1000000111111-1-1-1000000000
χ10222222222-2-2-22-1222-122-2-1-1-111-2-2-1-1-1-11111112-1-12-1-1000000-2-211112-1-1000000000
χ11222222222-2-2-22-1222-122-2-1-1-111-2-2-1-1-1-1111111-12-1-12-100000011-2-211-12-1000000000
χ12222222222-2-2-22-1222-122-2-1-1-111-2-2-1-1-1-1111111-1-12-1-120000001111-2-2-1-12000000000
χ13222222-2-2-2000-222-2-22220-2-2-20000222-2000000222222000000000000-2-2-2000000000
χ14222222-2-2-2000-222-2-22220-2-2-20000222-2000000-1-1-1-1-1-1000000−i3i3−i3i3−i3i3111000000000
χ15222222-2-2-2000-222-2-22220-2-2-20000222-2000000-1-1-1-1-1-1000000i3−i3i3−i3i3−i3111000000000
χ16222222-2-2-2000-2-12-2-2-1220111−i3i300-1-1-11−i3−i3−i3i3i3i32-1-12-1-100000000−i3i3i3−i3-211000000000
χ17222222-2-2-2000-2-12-2-2-1220111−i3i300-1-1-11−i3−i3−i3i3i3i3-12-1-12-1000000i3−i300−i3i31-21000000000
χ18222222-2-2-2000-2-12-2-2-1220111−i3i300-1-1-11−i3−i3−i3i3i3i3-1-12-1-12000000−i3i3i3−i30011-2000000000
χ19222222-2-2-2000-2-12-2-2-1220111i3−i300-1-1-11i3i3i3−i3−i3−i32-1-12-1-100000000i3−i3−i3i3-211000000000
χ20222222-2-2-2000-2-12-2-2-1220111i3−i300-1-1-11i3i3i3−i3−i3−i3-12-1-12-1000000−i3i300i3−i31-21000000000
χ21222222-2-2-2000-2-12-2-2-1220111i3−i300-1-1-11i3i3i3−i3−i3−i3-1-12-1-12000000i3−i3−i3i30011-2000000000
χ22333333333333-13-1-1-13-1-1-1-1-1-133-1-1-1-1-13-1-1-1-1-1-1000000111111000000000-1-1-1-11-1-111
χ23333333333333-13-1-1-13-1-1-1-1-1-133-1-1-1-1-13-1-1-1-1-1-1000000-1-1-1-1-1-10000000001111-111-1-1
χ24333333333-3-3-3-13-1-1-13-1-11-1-1-1-3-311-1-1-13111111000000111111000000000111-1-1-1-1-1-1
χ25333333333-3-3-3-13-1-1-13-1-11-1-1-1-3-311-1-1-13111111000000-1-1-1-1-1-1000000000-1-1-1111111
χ2633−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i323−3−3i32−3+3i32303−3−3i32−3+3i320−3−3i32−3+3i32300000−3−3i32−3+3i32000000000000000011−1−i32−1−i32−1+i32−1+i320000000001−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i32
χ2733−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i323−3−3i32−3+3i32303−3−3i32−3+3i320−3−3i32−3+3i32300000−3−3i32−3+3i320000000000000000-1-11+i321+i321−i321−i32000000000-11+i321−i32-1-11+i321−i321+i321−i32
χ2833−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i323−3−3i32−3+3i32-10-11+i321−i3201+i321−i32-12−1−i3−1+i3001+i321−i322−1−i3−1+i302−1−i3−1+i32−1−i3−1+i300000011−1−i32−1−i32−1+i32−1+i32000000000-11+i321−i32-111+i321−i32−1−i32−1+i32
χ2933−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i323−3−3i32−3+3i32-10-11+i321−i3201+i321−i32-12−1−i3−1+i3001+i321−i322−1−i3−1+i302−1−i3−1+i32−1−i3−1+i3000000-1-11+i321+i321−i321−i320000000001−1−i32−1+i321-1−1−i32−1+i321+i321−i32
χ3033−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32-33+3i323−3i32303−3−3i32−3+3i320−3−3i32−3+3i32-3000003+3i323−3i32000000000000000011−1−i32−1−i32−1+i32−1+i32000000000-11+i321−i321-1−1−i32−1+i321+i321−i32
χ3133−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32-33+3i323−3i32303−3−3i32−3+3i320−3−3i32−3+3i32-3000003+3i323−3i320000000000000000-1-11+i321+i321−i321−i320000000001−1−i32−1+i32-111+i321−i32−1−i32−1+i32
χ3233−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32-33+3i323−3i32-10-11+i321−i3201+i321−i3212−1−i3−1+i300−1−i32−1+i322−1−i3−1+i30-21+i31−i3-21+i31−i300000011−1−i32−1−i32−1+i32−1+i320000000001−1−i32−1+i32-1-11+i321−i321+i321−i32
χ3333−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32-33+3i323−3i32-10-11+i321−i3201+i321−i3212−1−i3−1+i300−1−i32−1+i322−1−i3−1+i30-21+i31−i3-21+i31−i3000000-1-11+i321+i321−i321−i32000000000-11+i321−i3211−1−i32−1+i32−1−i32−1+i32
χ3433−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i32303−3+3i32−3−3i320−3+3i32−3−3i32300000−3+3i32−3−3i32000000000000000011−1+i32−1+i32−1−i32−1−i320000000001−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i32
χ3533−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i32303−3+3i32−3−3i320−3+3i32−3−3i32300000−3+3i32−3−3i320000000000000000-1-11−i321−i321+i321+i32000000000-11−i321+i32-1-11−i321+i321−i321+i32
χ3633−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i32-10-11−i321+i3201−i321+i32-12−1+i3−1−i3001−i321+i322−1+i3−1−i302−1+i3−1−i32−1+i3−1−i300000011−1+i32−1+i32−1−i32−1−i32000000000-11−i321+i32-111−i321+i32−1+i32−1−i32
χ3733−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i32-10-11−i321+i3201−i321+i32-12−1+i3−1−i3001−i321+i322−1+i3−1−i302−1+i3−1−i32−1+i3−1−i3000000-1-11−i321−i321+i321+i320000000001−1+i32−1−i321-1−1+i32−1−i321−i321+i32
χ3833−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32-33−3i323+3i32303−3+3i32−3−3i320−3+3i32−3−3i32-3000003−3i323+3i32000000000000000011−1+i32−1+i32−1−i32−1−i32000000000-11−i321+i321-1−1+i32−1−i321−i321+i32
χ3933−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32-33−3i323+3i32303−3+3i32−3−3i320−3+3i32−3−3i32-3000003−3i323+3i320000000000000000-1-11−i321−i321+i321+i320000000001−1+i32−1−i32-111−i321+i32−1+i32−1−i32
χ4033−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32-33−3i323+3i32-10-11−i321+i3201−i321+i3212−1+i3−1−i300−1+i32−1−i322−1+i3−1−i30-21−i31+i3-21−i31+i300000011−1+i32−1+i32−1−i32−1−i320000000001−1+i32−1−i32-1-11−i321+i321−i321+i32
χ4133−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32-33−3i323+3i32-10-11−i321+i3201−i321+i3212−1+i3−1−i300−1+i32−1−i322−1+i3−1−i30-21−i31+i3-21−i31+i3000000-1-11−i321−i321+i321+i32000000000-11−i321+i3211−1+i32−1−i32−1+i32−1−i32
χ424-444-4-400000004000-400000000000000000000-2-2-22222i−2i2i−2i2i−2i000000000000000000
χ434-444-4-400000004000-400000000000000000000-2-2-2222−2i2i−2i2i−2i2i000000000000000000
χ44666666666666-2-3-2-2-2-3-2-2-2111-3-3-2-2111-3111111000000000000000000000000000000
χ45666666666-6-6-6-2-3-2-2-2-3-2-221113322111-3-1-1-1-1-1-1000000000000000000000000000000
χ46666666-6-6-600026-2226-2-202220000-2-2-2-6000000000000000000000000000000000000
χ47666666-6-6-60002-3-222-3-2-20-1-1-1−3i33i3001113i3i3i3−i3−i3−i3000000000000000000000000000000
χ48666666-6-6-60002-3-222-3-2-20-1-1-13i3−3i3001113−i3−i3−i3i3i3i3000000000000000000000000000000
χ4966−3−3i3−3+3i3−3−3i3−3+3i36−3−3i3−3+3i36−3−3i3−3+3i3-20-21+i31−i301+i31−i3-2-21+i31−i3001+i31−i3-21+i31−i30-21+i31−i3-21+i31−i3000000000000000000000000000000
χ5066−3−3i3−3+3i3−3−3i3−3+3i36−3−3i3−3+3i3-63+3i33−3i3-20-21+i31−i301+i31−i32-21+i31−i300−1−i3−1+i3-21+i31−i302−1−i3−1+i32−1−i3−1+i3000000000000000000000000000000
χ5166−3−3i3−3+3i3−3−3i3−3+3i3-63+3i33−3i300020-2−1−i3−1+i301+i31−i302−1−i3−1+i30000-21+i31−i30−2i3−3+i33+i32i33−i3−3−i3000000000000000000000000000000
χ5266−3−3i3−3+3i3−3−3i3−3+3i3-63+3i33−3i300020-2−1−i3−1+i301+i31−i302−1−i3−1+i30000-21+i31−i302i33−i3−3−i3−2i3−3+i33+i3000000000000000000000000000000
χ5366−3−3i3−3+3i3−3−3i3−3+3i3-63+3i33−3i300020-2−1−i3−1+i301+i31−i30-42+2i32−2i300004−2−2i3−2+2i30000000000000000000000000000000000000
χ5466−3−3i3−3+3i3−3−3i3−3+3i3-63+3i33−3i3000-6063+3i33−3i30−3−3i3−3+3i3000000000000000000000000000000000000000000000000
χ5566−3+3i3−3−3i3−3+3i3−3−3i36−3+3i3−3−3i36−3+3i3−3−3i3-20-21−i31+i301−i31+i3-2-21−i31+i3001−i31+i3-21−i31+i30-21−i31+i3-21−i31+i3000000000000000000000000000000
χ5666−3+3i3−3−3i3−3+3i3−3−3i36−3+3i3−3−3i3-63−3i33+3i3-20-21−i31+i301−i31+i32-21−i31+i300−1+i3−1−i3-21−i31+i302−1+i3−1−i32−1+i3−1−i3000000000000000000000000000000
χ5766−3+3i3−3−3i3−3+3i3−3−3i3-63−3i33+3i300020-2−1+i3−1−i301−i31+i302−1+i3−1−i30000-21−i31+i30−2i33+i3−3+i32i3−3−i33−i3000000000000000000000000000000
χ5866−3+3i3−3−3i3−3+3i3−3−3i3-63−3i33+3i300020-2−1+i3−1−i301−i31+i302−1+i3−1−i30000-21−i31+i302i3−3−i33−i3−2i33+i3−3+i3000000000000000000000000000000
χ5966−3+3i3−3−3i3−3+3i3−3−3i3-63−3i33+3i300020-2−1+i3−1−i301−i31+i30-42−2i32+2i300004−2+2i3−2−2i30000000000000000000000000000000000000
χ6066−3+3i3−3−3i3−3+3i3−3−3i3-63−3i33+3i3000-6063−3i33+3i30−3+3i3−3−3i3000000000000000000000000000000000000000000000000
χ618-888-8-800000008000-800000000000000000000222-2-2-2000000000000000000000000
χ628-888-8-80000000-400040000000000000000000022-4-2-24000000000000000000000000
χ638-888-8-80000000-40004000000000000000000002-42-24-2000000000000000000000000
χ648-888-8-80000000-4000400000000000000000000-4224-2-2000000000000000000000000
χ6512-12−6−6i3−6+6i36+6i36−6i3000000000000000000000000000000000000002i−2i2ζ11−2ζ112ζ7−2ζ7000000000000000000
χ6612-12−6−6i3−6+6i36+6i36−6i300000000000000000000000000000000000000−2i2i−2ζ112ζ11−2ζ72ζ7000000000000000000
χ6712-12−6+6i3−6−6i36−6i36+6i3000000000000000000000000000000000000002i−2i2ζ7−2ζ72ζ11−2ζ11000000000000000000
χ6812-12−6+6i3−6−6i36−6i36+6i300000000000000000000000000000000000000−2i2i−2ζ72ζ7−2ζ112ζ11000000000000000000

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