Finite Group Databasebeta

← Group #88498

Character table — Group #88498

Order 432.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222333333336666666666666666666666666666181818181818181818181818
order122234466612121212336666669991212121218181818181818181836363636363636363636363644441212121212121212
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ411111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-1-1-11+i321+i321−i321−i321+i321+i321−i321−i32
χ511111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ611111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-1-1-11−i321−i321+i321+i321−i321−i321+i321+i32
χ711111-1-1111-1-1-1-111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ811111-1-1111-1-1-1-111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ911111-1-1111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321−1−i32−1+i321+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i3211-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32
χ1011111-1-1111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321−1−i32−1+i321+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32-1-1111+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32
χ1111111-1-1111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−1+i32−1−i321−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i3211-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32
χ1211111-1-1111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−1+i32−1−i321−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32-1-1111−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32
χ131-11-11i−i1-1-1ii−i−i11-1-111-1-1111i−ii−i1-11-11-1-1-1-1ii−i−iii−i−iii−i−i1-1i−i1-11-1i−ii−i
χ141-11-11i−i1-1-1ii−i−i11-1-111-1-1111i−ii−i1-11-11-1-1-1-1ii−i−iii−i−iii−i−i-11−ii-11-11−ii−ii
χ151-11-11i−i1-1-1ii−i−i−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i321−1−i32−1+i32ζ11−ζ11ζ7−ζ71-1−1−i321+i32−1+i321−i32-11+i321−i32ii−i−iζ11ζ11−ζ11−ζ11ζ7ζ7−ζ7−ζ71-1i−i−1−i321+i32−1+i321−i32ζ11−ζ11ζ7−ζ7
χ161-11-11i−i1-1-1ii−i−i−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i321−1−i32−1+i32ζ11−ζ11ζ7−ζ71-1−1−i321+i32−1+i321−i32-11+i321−i32ii−i−iζ11ζ11−ζ11−ζ11ζ7ζ7−ζ7−ζ7-11−ii1+i32−1−i321−i32−1+i32−ζ11ζ11−ζ7ζ7
χ171-11-11i−i1-1-1ii−i−i−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i321−1+i32−1−i32ζ7−ζ7ζ11−ζ111-1−1+i321−i32−1−i321+i32-11−i321+i32ii−i−iζ7ζ7−ζ7−ζ7ζ11ζ11−ζ11−ζ111-1i−i−1+i321−i32−1−i321+i32ζ7−ζ7ζ11−ζ11
χ181-11-11i−i1-1-1ii−i−i−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i321−1+i32−1−i32ζ7−ζ7ζ11−ζ111-1−1+i321−i32−1−i321+i32-11−i321+i32ii−i−iζ7ζ7−ζ7−ζ7ζ11ζ11−ζ11−ζ11-11−ii1−i32−1+i321+i32−1−i32−ζ7ζ7−ζ11ζ11
χ191-11-11−ii1-1-1−i−iii11-1-111-1-1111−ii−ii1-11-11-1-1-1-1−i−iii−i−iii−i−iii1-1−ii1-11-1−ii−ii
χ201-11-11−ii1-1-1−i−iii11-1-111-1-1111−ii−ii1-11-11-1-1-1-1−i−iii−i−iii−i−iii-11i−i-11-11i−ii−i
χ211-11-11−ii1-1-1−i−iii−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i321−1−i32−1+i32−ζ11ζ11−ζ7ζ71-1−1−i321+i32−1+i321−i32-11+i321−i32−i−iii−ζ11−ζ11ζ11ζ11−ζ7−ζ7ζ7ζ71-1−ii−1−i321+i32−1+i321−i32−ζ11ζ11−ζ7ζ7
χ221-11-11−ii1-1-1−i−iii−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i321−1−i32−1+i32−ζ11ζ11−ζ7ζ71-1−1−i321+i32−1+i321−i32-11+i321−i32−i−iii−ζ11−ζ11ζ11ζ11−ζ7−ζ7ζ7ζ7-11i−i1+i32−1−i321−i32−1+i32ζ11−ζ11ζ7−ζ7
χ231-11-11−ii1-1-1−i−iii−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i321−1+i32−1−i32−ζ7ζ7−ζ11ζ111-1−1+i321−i32−1−i321+i32-11−i321+i32−i−iii−ζ7−ζ7ζ7ζ7−ζ11−ζ11ζ11ζ111-1−ii−1+i321−i32−1−i321+i32−ζ7ζ7−ζ11ζ11
χ241-11-11−ii1-1-1−i−iii−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i321−1+i32−1−i32−ζ7ζ7−ζ11ζ111-1−1+i321−i32−1−i321+i32-11−i321+i32−i−iii−ζ7−ζ7ζ7ζ7−ζ11−ζ11ζ11ζ11-11i−i1−i32−1+i321+i32−1−i32ζ7−ζ7ζ11−ζ11
χ252222222222222222222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ2622222222222222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3-11+i321−i32−1−i3−1−i3−1+i3−1+i3-1-11+i321+i321−i321−i32-11+i321−i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32000000000000
χ2722222222222222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3-11−i321+i32−1+i3−1+i3−1−i3−1−i3-1-11−i321−i321+i321+i32-11−i321+i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32000000000000
χ2822222-2-2222-2-2-2-222222222-1-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1111111111111000000000000
χ2922222-2-2222-2-2-2-2−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3-11+i321−i321+i31+i31−i31−i3-1-11+i321+i321−i321−i32-11+i321−i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32000000000000
χ3022222-2-2222-2-2-2-2−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3-11−i321+i321−i31−i31+i31+i3-1-11−i321−i321+i321+i32-11−i321+i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32000000000000
χ3122-2-2200-22-200002222-2-2-2-22220000-22-22-22-2-2-2000000000000000000000000
χ3222-2-2200-22-200002222-2-2-2-2-1-1-100001-11-11-11113−33−33−33−33−33−3000000000000
χ3322-2-2200-22-200002222-2-2-2-2-1-1-100001-11-11-1111−33−33−33−33−33−33000000000000
χ3422-2-2200-22-20000−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i32−1−i3−1+i30000-221+i3−1−i31−i3−1+i3-21+i31−i3000000000000000000000000
χ3522-2-2200-22-20000−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i3-11+i321−i3200001-1−1−i321+i32−1+i321−i321−1−i32−1+i323−33−32ζ7+ζ11−2ζ7−ζ112ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ11−ζ7−2ζ11ζ7+2ζ11000000000000
χ3622-2-2200-22-20000−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i3-11+i321−i3200001-1−1−i321+i32−1+i321−i321−1−i32−1+i32−33−33−2ζ7−ζ112ζ7+ζ11−2ζ7−ζ112ζ7+ζ11ζ7+2ζ11−ζ7−2ζ11ζ7+2ζ11−ζ7−2ζ11000000000000
χ3722-2-2200-22-20000−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i32−1+i3−1−i30000-221−i3−1+i31+i3−1−i3-21−i31+i3000000000000000000000000
χ3822-2-2200-22-20000−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i3-11−i321+i3200001-1−1+i321−i32−1−i321+i321−1+i32−1−i323−33−3−ζ7−2ζ11ζ7+2ζ11−ζ7−2ζ11ζ7+2ζ112ζ7+ζ11−2ζ7−ζ112ζ7+ζ11−2ζ7−ζ11000000000000
χ3922-2-2200-22-20000−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i3-11−i321+i3200001-1−1+i321−i32−1−i321+i321−1+i32−1−i32−33−33ζ7+2ζ11−ζ7−2ζ11ζ7+2ζ11−ζ7−2ζ11−2ζ7−ζ112ζ7+ζ11−2ζ7−ζ112ζ7+ζ11000000000000
χ402-22-222i−2i2-2-22i2i−2i−2i22-2-222-2-2-1-1-12i−2i2i−2i-11-11-11111−i−iii−i−iii−i−iii000000000000
χ412-22-222i−2i2-2-22i2i−2i−2i−1−i3−1+i31+i31−i3−1−i3−1+i31+i31−i3-11+i321−i322ζ11−2ζ112ζ7−2ζ7-111+i32−1−i321−i32−1+i321−1−i32−1+i32−i−iii−ζ11−ζ11ζ11ζ11−ζ7−ζ7ζ7ζ7000000000000
χ422-22-222i−2i2-2-22i2i−2i−2i−1+i3−1−i31−i31+i3−1+i3−1−i31−i31+i3-11−i321+i322ζ7−2ζ72ζ11−2ζ11-111−i32−1+i321+i32−1−i321−1+i32−1−i32−i−iii−ζ7−ζ7ζ7ζ7−ζ11−ζ11ζ11ζ11000000000000
χ432-22-22−2i2i2-2-2−2i−2i2i2i22-2-222-2-2-1-1-1−2i2i−2i2i-11-11-11111ii−i−iii−i−iii−i−i000000000000
χ442-22-22−2i2i2-2-2−2i−2i2i2i−1−i3−1+i31+i31−i3−1−i3−1+i31+i31−i3-11+i321−i32−2ζ112ζ11−2ζ72ζ7-111+i32−1−i321−i32−1+i321−1−i32−1+i32ii−i−iζ11ζ11−ζ11−ζ11ζ7ζ7−ζ7−ζ7000000000000
χ452-22-22−2i2i2-2-2−2i−2i2i2i−1+i3−1−i31−i31+i3−1+i3−1−i31−i31+i3-11−i321+i32−2ζ72ζ7−2ζ112ζ11-111−i32−1+i321+i32−1−i321−1+i32−1−i32ii−i−iζ7ζ7−ζ7−ζ7ζ11ζ11−ζ11−ζ11000000000000
χ462-2-22200-2-22000022-2-2-2-2222220000-2-2-2-2-2-2222000000000000000000000000
χ472-2-22200-2-22000022-2-2-2-222-1-1-10000111111-1-1-1−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3000000000000
χ482-2-22200-2-22000022-2-2-2-222-1-1-10000111111-1-1-1i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3000000000000
χ492-2-22200-2-220000−1−i3−1+i31+i31−i31+i31−i3−1−i3−1+i32−1−i3−1+i30000-2-21+i31+i31−i31−i32−1−i3−1+i3000000000000000000000000
χ502-2-22200-2-220000−1−i3−1+i31+i31−i31+i31−i3−1−i3−1+i3-11+i321−i32000011−1−i32−1−i32−1+i32−1+i32-11+i321−i32−i3i3i3−i3−3+i323−i323−i32−3+i323+i32−3−i32−3−i323+i32000000000000
χ512-2-22200-2-220000−1−i3−1+i31+i31−i31+i31−i3−1−i3−1+i3-11+i321−i32000011−1−i32−1−i32−1+i32−1+i32-11+i321−i32i3−i3−i3i33−i32−3+i32−3+i323−i32−3−i323+i323+i32−3−i32000000000000
χ522-2-22200-2-220000−1+i3−1−i31−i31+i31−i31+i3−1+i3−1−i32−1+i3−1−i30000-2-21−i31−i31+i31+i32−1+i3−1−i3000000000000000000000000
χ532-2-22200-2-220000−1+i3−1−i31−i31+i31−i31+i3−1+i3−1−i3-11−i321+i32000011−1+i32−1+i32−1−i32−1−i32-11−i321+i32−i3i3i3−i33+i32−3−i32−3−i323+i32−3+i323−i323−i32−3+i32000000000000
χ542-2-22200-2-220000−1+i3−1−i31−i31+i31−i31+i3−1+i3−1−i3-11−i321+i32000011−1+i32−1+i32−1−i32−1−i32-11−i321+i32i3−i3−i3i3−3−i323+i323+i32−3−i323−i32−3+i32−3+i323−i32000000000000
χ556666-366-3-3-3-3-3-3-3000000000000000000000000000000000000000000000000
χ566666-3-6-6-3-3-33333000000000000000000000000000000000000000000000000
χ5766-6-6-3003-3333−3333−33000000000000000000000000000000000000000000000000
χ5866-6-6-3003-33−3333−3333000000000000000000000000000000000000000000000000
χ596-66-6-36i−6i-333−3i−3i3i3i000000000000000000000000000000000000000000000000
χ606-66-6-3−6i6i-3333i3i−3i−3i000000000000000000000000000000000000000000000000
χ616-6-66-30033-3−3i33i33i3−3i3000000000000000000000000000000000000000000000000
χ626-6-66-30033-33i3−3i3−3i33i3000000000000000000000000000000000000000000000000

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