Finite Group Databasebeta

← Group #13047378

Character table — Group #13047378

Order 1296.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size112222244466666666999912121212121212121212121218181818181818181818272727272727363636363636545454545454545454
order12344461212123333666633661212121212121212121212129912121212121218184412121212363636363636222666666
χ111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1
χ3111111111111111111−1−i32−1+i32−1−i32−1+i32111111111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32
χ4111111111111111111−1−i32−1+i32−1−i32−1+i32111111111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+i32-1-11+i321+i321−i321−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1-11+i321+i321+i321−i321−i321−i32
χ5111111111111111111−1+i32−1−i32−1+i32−1−i32111111111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32
χ6111111111111111111−1+i32−1−i32−1+i32−1−i32111111111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i32-1-11−i321−i321+i321+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1-11−i321−i321−i321+i321+i321+i32
χ71111-1-111-1-11111111111111111-1-1-1-1-1-1-1-1111-1-11-1-1111111111-1-11-1-11-1-11-1-11-1-1
χ81111-1-111-1-11111111111111111-1-1-1-1-1-1-1-1111-1-11-1-111-1-1-1-1-1-11-1-11-1-1-111-111-111
χ91111-1-111-1-111111111−1−i32−1+i32−1−i32−1+i321111-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i321+i321+i32−1+i321−i321−i321-1-1−1−i321+i321+i32−1+i321−i321−i32
χ101111-1-111-1-111111111−1−i32−1+i32−1−i32−1+i321111-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i32−1−i32−1+i32-1-11+i321+i321−i321−i32−1−i321+i321+i32−1+i321−i321−i32-1111+i32−1−i32−1−i321−i32−1+i32−1+i32
χ111111-1-111-1-111111111−1+i32−1−i32−1+i32−1−i321111-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i321−i321−i32−1−i321+i321+i321-1-1−1+i321−i321−i32−1−i321+i321+i32
χ121111-1-111-1-111111111−1+i32−1−i32−1+i32−1−i321111-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32−1+i32−1−i32-1-11−i321−i321+i321+i32−1+i321−i321−i32−1−i321+i321+i32-1111−i32−1+i32−1+i321+i32−1−i32−1−i32
χ13111-11-11-11-1111111111111-1-1-1-11111-1-1-1-111-11-1-11-111111111-11-1-11-1-11-1-11-1-11-1
χ14111-11-11-11-1111111111111-1-1-1-11111-1-1-1-111-11-1-11-111-1-1-1-1-1-1-11-1-11-11-111-111-11
χ15111-11-11-11-111111111−1−i32−1+i32−1−i32−1+i32-1-1-1-11111-1-1-1-1−1−i32−1+i321+i32−1−i321+i321−i32−1+i321−i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321+i32−1−i321+i321−i32−1+i321−i32-11-11+i32−1−i321+i321−i32−1+i321−i32
χ16111-11-11-11-111111111−1−i32−1+i32−1−i32−1+i32-1-1-1-11111-1-1-1-1−1−i32−1+i321+i32−1−i321+i321−i32−1+i321−i32−1−i32−1+i32-1-11+i321+i321−i321−i321+i32−1−i321+i321−i32−1+i321−i321-11−1−i321+i32−1−i32−1+i321−i32−1+i32
χ17111-11-11-11-111111111−1+i32−1−i32−1+i32−1−i32-1-1-1-11111-1-1-1-1−1+i32−1−i321−i32−1+i321−i321+i32−1−i321+i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−i32−1+i321−i321+i32−1−i321+i32-11-11−i32−1+i321−i321+i32−1−i321+i32
χ18111-11-11-11-111111111−1+i32−1−i32−1+i32−1−i32-1-1-1-11111-1-1-1-1−1+i32−1−i321−i32−1+i321−i321+i32−1−i321+i32−1+i32−1−i32-1-11−i321−i321+i321+i321−i32−1+i321−i321+i32−1−i321+i321-11−1+i321−i32−1+i32−1−i321+i32−1−i32
χ19111-1-111-1-11111111111111-1-1-1-1-1-1-1-1111111-1-11-1-1111111111-1-11-1-11-1-11-1-11-1-11
χ20111-1-111-1-11111111111111-1-1-1-1-1-1-1-1111111-1-11-1-1111-1-1-1-1-1-1-1-11-1-1111-111-111-1
χ21111-1-111-1-1111111111−1−i32−1+i32−1−i32−1+i32-1-1-1-1-1-1-1-11111−1−i32−1+i321+i321+i32−1−i321−i321−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321+i321+i32−1−i321−i321−i32−1+i32-1-111+i321+i32−1−i321−i321−i32−1+i32
χ22111-1-111-1-1111111111−1−i32−1+i32−1−i32−1+i32-1-1-1-1-1-1-1-11111−1−i32−1+i321+i321+i32−1−i321−i321−i32−1+i32−1−i32−1+i32-1-11+i321+i321−i321−i321+i321+i32−1−i321−i321−i32−1+i3211-1−1−i32−1−i321+i32−1+i32−1+i321−i32
χ23111-1-111-1-1111111111−1+i32−1−i32−1+i32−1−i32-1-1-1-1-1-1-1-11111−1+i32−1−i321−i321−i32−1+i321+i321+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−i321−i32−1+i321+i321+i32−1−i32-1-111−i321−i32−1+i321+i321+i32−1−i32
χ24111-1-111-1-1111111111−1+i32−1−i32−1+i32−1−i32-1-1-1-1-1-1-1-11111−1+i32−1−i321−i321−i32−1+i321+i321+i32−1−i32−1+i32−1−i32-1-11−i321−i321+i321+i321−i321−i32−1+i321+i321+i32−1−i3211-1−1+i32−1+i321−i32−1−i32−1−i321+i32
χ2522222222222-1-1-12-1-1-122222-1-1-12-1-1-12-1-1-1-1-1222222-1-1000000-1-1-1-1-1-1000000000
χ2622222222222-1-1-12-1-1-1−1−i3−1+i3−1−i3−1+i32-1-1-12-1-1-12-1-1-11+i321−i32−1−i3−1−i3−1−i3−1+i3−1+i3−1+i31+i321−i320000001+i321+i321+i321−i321−i321−i32000000000
χ2722222222222-1-1-12-1-1-1−1+i3−1−i3−1+i3−1−i32-1-1-12-1-1-12-1-1-11−i321+i32−1+i3−1+i3−1+i3−1−i3−1−i3−1−i31−i321+i320000001−i321−i321−i321+i321+i321+i32000000000
χ282222-2-222-2-22-1-1-12-1-1-122222-1-1-1-2111-2111-1-12-2-22-2-2-1-1000000-111-111000000000
χ292222-2-222-2-22-1-1-12-1-1-1−1−i3−1+i3−1−i3−1+i32-1-1-1-2111-21111+i321−i32−1−i31+i31+i3−1+i31−i31−i31+i321−i320000001+i32−1−i32−1−i321−i32−1+i32−1+i32000000000
χ302222-2-222-2-22-1-1-12-1-1-1−1+i3−1−i3−1+i3−1−i32-1-1-1-2111-21111−i321+i32−1+i31−i31−i3−1−i31+i31+i31−i321+i320000001−i32−1+i32−1+i321+i32−1−i32−1−i32000000000
χ31222-22-22-22-22-1-1-12-1-1-12222-21112-1-1-1-2111-1-1-22-2-22-2-1-10000001-111-11000000000
χ32222-22-22-22-22-1-1-12-1-1-1−1−i3−1+i3−1−i3−1+i3-21112-1-1-1-21111+i321−i321+i3−1−i31+i31−i3−1+i31−i31+i321−i32000000−1−i321+i32−1−i32−1+i321−i32−1+i32000000000
χ33222-22-22-22-22-1-1-12-1-1-1−1+i3−1−i3−1+i3−1−i3-21112-1-1-1-21111−i321+i321−i3−1+i31−i31+i3−1−i31+i31−i321+i32000000−1+i321−i32−1+i32−1−i321+i32−1−i32000000000
χ34222-2-222-2-222-1-1-12-1-1-12222-2111-21112-1-1-1-1-1-2-22-2-22-1-100000011-111-1000000000
χ35222-2-222-2-222-1-1-12-1-1-1−1−i3−1+i3−1−i3−1+i3-2111-21112-1-1-11+i321−i321+i31+i3−1−i31−i31−i3−1+i31+i321−i32000000−1−i32−1−i321+i32−1+i32−1+i321−i32000000000
χ36222-2-222-2-222-1-1-12-1-1-1−1+i3−1−i3−1+i3−1−i3-2111-21112-1-1-11−i321+i321−i31−i3−1+i31+i31+i3−1−i31−i321+i32000000−1+i32−1+i321−i32−1−i32−1−i321+i32000000000
χ372-22000-20002222-2-2-2-222-2-200000000000022000000-2-22i−2i2i−2i2i−2i000000000000000
χ382-22000-20002222-2-2-2-222-2-200000000000022000000-2-2−2i2i−2i2i−2i2i000000000000000
χ392-22000-20002222-2-2-2-2−1−i3−1+i31+i31−i3000000000000−1−i3−1+i30000001+i31−i32i−2i2ζ11−2ζ112ζ7−2ζ7000000000000000
χ402-22000-20002222-2-2-2-2−1−i3−1+i31+i31−i3000000000000−1−i3−1+i30000001+i31−i3−2i2i−2ζ112ζ11−2ζ72ζ7000000000000000
χ412-22000-20002222-2-2-2-2−1+i3−1−i31−i31+i3000000000000−1+i3−1−i30000001−i31+i32i−2i2ζ7−2ζ72ζ11−2ζ11000000000000000
χ422-22000-20002222-2-2-2-2−1+i3−1−i31−i31+i3000000000000−1+i3−1−i30000001−i31+i3−2i2i−2ζ72ζ7−2ζ112ζ11000000000000000
χ434-44000-40004-2-2-2-422244-4-4000000000000-2-200000022000000000000000000000
χ444-44000-40004-2-2-2-4222−2−2i3−2+2i32+2i32−2i30000000000001+i31−i3000000−1−i3−1+i3000000000000000000000
χ454-44000-40004-2-2-2-4222−2+2i3−2−2i32−2i32+2i30000000000001−i31+i3000000−1+i3−1−i3000000000000000000000
χ466666666666-3000-30000000-3000-3000-30000000000000000000000000000000000
χ476666-6-666-6-6-3000-30000000-3000300030000000000000000000000000000000000
χ48666-66-66-66-6-3000-300000003000-300030000000000000000000000000000000000
χ49666-6-666-6-66-3000-3000000030003000-30000000000000000000000000000000000
χ5066-3666-3-3-3-3003-3003-30000003-3003-3003-30000000000000000000000000000000
χ5166-3666-3-3-3-303-3003-30000003-3003-3003-300000000000000000000000000000000
χ5266-3666-3-3-3-30-3030-30300000-3030-3030-3030000000000000000000000000000000
χ5366-36-6-6-3-333003-3003-30000003-300-3300-330000000000000000000000000000000
χ5466-36-6-6-3-33303-3003-30000003-300-3300-3300000000000000000000000000000000
χ5566-36-6-6-3-3330-3030-30300000-303030-3030-30000000000000000000000000000000
χ5666-3-66-6-33-33003-3003-3000000-33003-300-330000000000000000000000000000000
χ5766-3-66-6-33-3303-3003-3000000-33003-300-3300000000000000000000000000000000
χ5866-3-66-6-33-330-3030-3030000030-30-303030-30000000000000000000000000000000
χ5966-3-6-66-333-3003-3003-3000000-3300-33003-30000000000000000000000000000000
χ6066-3-6-66-333-303-3003-3000000-3300-33003-300000000000000000000000000000000
χ6166-3-6-66-333-30-3030-3030000030-3030-30-3030000000000000000000000000000000
χ6212-1212000-12000-6000600000000000000000000000000000000000000000000000000
χ6312-12-60006000006-600-6600000000000000000000000000000000000000000000000
χ6412-12-6000600006-600-66000000000000000000000000000000000000000000000000
χ6512-12-600060000-606060-600000000000000000000000000000000000000000000000

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