Finite Group Databasebeta

← Group #88705

Character table — Group #88705

Order 432.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11222223333666666666666661818181818181122222333366666666666666181818181818
order123461212336699912121818183636363636364412121212226461212666618181812121818183636363636364412121212
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111-1-1-1-1-1-11111111111111111111111111-1-1-1-1-1-1
χ31111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i321111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32
χ41111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i321111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32
χ51111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i321111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32
χ61111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i321111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32
χ7111-11-1-11111111-1-1111-1-1-1-1-1-11-11-11-1111-11-1-11111111-1-1111-1-1-1-1-1-11-11-11-1
χ8111-11-1-11111111-1-1111-1-1-1-1-1-1-11-11-11111-11-1-11111111-1-1111-1-1-1-1-1-1-11-11-11
χ9111-11-1-1−1−i32−1+i32−1−i32−1+i321−1−i32−1+i321+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i321-1−1−i321+i32−1+i321−i32111-11-1-1−1−i32−1+i32−1−i32−1+i321−1−i32−1+i321+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i321-1−1−i321+i32−1+i321−i32
χ10111-11-1-1−1−i32−1+i32−1−i32−1+i321−1−i32−1+i321+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i32-111+i32−1−i321−i32−1+i32111-11-1-1−1−i32−1+i32−1−i32−1+i321−1−i32−1+i321+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i32-111+i32−1−i321−i32−1+i32
χ11111-11-1-1−1+i32−1−i32−1+i32−1−i321−1+i32−1−i321−i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i321-1−1+i321−i32−1−i321+i32111-11-1-1−1+i32−1−i32−1+i32−1−i321−1+i32−1−i321−i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i321-1−1+i321−i32−1−i321+i32
χ12111-11-1-1−1+i32−1−i32−1+i32−1−i321−1+i32−1−i321−i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i32-111−i32−1+i321+i32−1−i32111-11-1-1−1+i32−1−i32−1+i32−1−i321−1+i32−1−i321−i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i32-111−i32−1+i321+i32−1−i32
χ1322222222222-1-1-122-1-1-1-1-1-1-1-1-100000022222222222-1-1-122-1-1-1-1-1-1-1-1-1000000
χ142222222−1−i3−1+i3−1−i3−1+i3-11+i321−i32−1−i3−1+i3-11+i321−i32-1-11+i321+i321−i321−i320000002222222−1−i3−1+i3−1−i3−1+i3-11+i321−i32−1−i3−1+i3-11+i321−i32-1-11+i321+i321−i321−i32000000
χ152222222−1+i3−1−i3−1+i3−1−i3-11−i321+i32−1+i3−1−i3-11−i321+i32-1-11−i321−i321+i321+i320000002222222−1+i3−1−i3−1+i3−1−i3-11−i321+i32−1+i3−1−i3-11−i321+i32-1-11−i321−i321+i321+i32000000
χ16222-22-2-22222-1-1-1-2-2-1-1-1111111000000222-22-2-22222-1-1-1-2-2-1-1-1111111000000
χ17222-22-2-2−1−i3−1+i3−1−i3−1+i3-11+i321−i321+i31−i3-11+i321−i3211−1−i32−1−i32−1+i32−1+i32000000222-22-2-2−1−i3−1+i3−1−i3−1+i3-11+i321−i321+i31−i3-11+i321−i3211−1−i32−1−i32−1+i32−1+i32000000
χ18222-22-2-2−1+i3−1−i3−1+i3−1−i3-11−i321+i321−i31+i3-11−i321+i3211−1+i32−1+i32−1−i32−1−i32000000222-22-2-2−1+i3−1−i3−1+i3−1−i3-11−i321+i321−i31+i3-11−i321+i3211−1+i32−1+i32−1−i32−1−i32000000
χ192-220-20022-2-222200-2-2-20000000000002-220-20022-2-222200-2-2-2000000000000
χ202-220-20022-2-2-1-1-1001113−33−33−30000002-220-20022-2-2-1-1-1001113−33−33−3000000
χ212-220-20022-2-2-1-1-100111−33−33−330000002-220-20022-2-2-1-1-100111−33−33−33000000
χ222-220-200−1−i3−1+i31+i31−i32−1−i3−1+i300-21+i31−i30000000000002-220-200−1−i3−1+i31+i31−i32−1−i3−1+i300-21+i31−i3000000000000
χ232-220-200−1−i3−1+i31+i31−i3-11+i321−i32001−1−i32−1+i323−32ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ110000002-220-200−1−i3−1+i31+i31−i3-11+i321−i32001−1−i32−1+i323−32ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ11000000
χ242-220-200−1−i3−1+i31+i31−i3-11+i321−i32001−1−i32−1+i32−33−2ζ7−ζ112ζ7+ζ11ζ7+2ζ11−ζ7−2ζ110000002-220-200−1−i3−1+i31+i31−i3-11+i321−i32001−1−i32−1+i32−33−2ζ7−ζ112ζ7+ζ11ζ7+2ζ11−ζ7−2ζ11000000
χ252-220-200−1+i3−1−i31−i31+i32−1+i3−1−i300-21−i31+i30000000000002-220-200−1+i3−1−i31−i31+i32−1+i3−1−i300-21−i31+i3000000000000
χ262-220-200−1+i3−1−i31−i31+i3-11−i321+i32001−1+i32−1−i323−3−ζ7−2ζ11ζ7+2ζ112ζ7+ζ11−2ζ7−ζ110000002-220-200−1+i3−1−i31−i31+i3-11−i321+i32001−1+i32−1−i323−3−ζ7−2ζ11ζ7+2ζ112ζ7+ζ11−2ζ7−ζ11000000
χ272-220-200−1+i3−1−i31−i31+i3-11−i321+i32001−1+i32−1−i32−33ζ7+2ζ11−ζ7−2ζ11−2ζ7−ζ112ζ7+ζ110000002-220-200−1+i3−1−i31−i31+i3-11−i321+i32001−1+i32−1−i32−33ζ7+2ζ11−ζ7−2ζ11−2ζ7−ζ112ζ7+ζ11000000
χ2866-36-3-3-300000000000000000000000066-36-3-3-3000000000000000000000000
χ2966-3-6-33300000000000000000000000066-3-6-333000000000000000000000000
χ306-6-30333−330000000000000000000000006-6-30333−33000000000000000000000000
χ316-6-303−33330000000000000000000000006-6-303−3333000000000000000000000000
χ321111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ331111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ341111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-1-1-1-1-1-11+i321−i321+i321−i32-11+i321−i321+i321−i32-11+i321−i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32
χ351111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32-1-1-1-1-1-1-11+i321−i321+i321−i32-11+i321−i321+i321−i32-11+i321−i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32
χ361111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-1-1-1-1-1-11−i321+i321−i321+i32-11−i321+i321−i321+i32-11−i321+i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32
χ371111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32-1-1-1-1-1-1-11−i321+i321−i321+i32-11−i321+i321−i321+i32-11−i321+i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32
χ38111-11-1-11111111-1-1111-1-1-1-1-1-11-11-11-1-1-1-11-111-1-1-1-1-1-1-111-1-1-1111111-11-11-11
χ39111-11-1-11111111-1-1111-1-1-1-1-1-1-11-11-11-1-1-11-111-1-1-1-1-1-1-111-1-1-11111111-11-11-1
χ40111-11-1-1−1−i32−1+i32−1−i32−1+i321−1−i32−1+i321+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i321-1−1−i321+i32−1+i321−i32-1-1-11-1111+i321−i321+i321−i32-11+i321−i32−1−i32−1+i32-11+i321−i3211−1−i32−1−i32−1+i32−1+i32-111+i32−1−i321−i32−1+i32
χ41111-11-1-1−1−i32−1+i32−1−i32−1+i321−1−i32−1+i321+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i32-111+i32−1−i321−i32−1+i32-1-1-11-1111+i321−i321+i321−i32-11+i321−i32−1−i32−1+i32-11+i321−i3211−1−i32−1−i32−1+i32−1+i321-1−1−i321+i32−1+i321−i32
χ42111-11-1-1−1+i32−1−i32−1+i32−1−i321−1+i32−1−i321−i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i321-1−1+i321−i32−1−i321+i32-1-1-11-1111−i321+i321−i321+i32-11−i321+i32−1+i32−1−i32-11−i321+i3211−1+i32−1+i32−1−i32−1−i32-111−i32−1+i321+i32−1−i32
χ43111-11-1-1−1+i32−1−i32−1+i32−1−i321−1+i32−1−i321−i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i32-111−i32−1+i321+i32−1−i32-1-1-11-1111−i321+i321−i321+i32-11−i321+i32−1+i32−1−i32-11−i321+i3211−1+i32−1+i32−1−i32−1−i321-1−1+i321−i32−1−i321+i32
χ4422222222222-1-1-122-1-1-1-1-1-1-1-1-1000000-2-2-2-2-2-2-2-2-2-2-2111-2-2111111111000000
χ452222222−1−i3−1+i3−1−i3−1+i3-11+i321−i32−1−i3−1+i3-11+i321−i32-1-11+i321+i321−i321−i32000000-2-2-2-2-2-2-21+i31−i31+i31−i31−1−i32−1+i321+i31−i31−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32000000
χ462222222−1+i3−1−i3−1+i3−1−i3-11−i321+i32−1+i3−1−i3-11−i321+i32-1-11−i321−i321+i321+i32000000-2-2-2-2-2-2-21−i31+i31−i31+i31−1+i32−1−i321−i31+i31−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32000000
χ47222-22-2-22222-1-1-1-2-2-1-1-1111111000000-2-2-22-222-2-2-2-211122111-1-1-1-1-1-1000000
χ48222-22-2-2−1−i3−1+i3−1−i3−1+i3-11+i321−i321+i31−i3-11+i321−i3211−1−i32−1−i32−1+i32−1+i32000000-2-2-22-2221+i31−i31+i31−i31−1−i32−1+i32−1−i3−1+i31−1−i32−1+i32-1-11+i321+i321−i321−i32000000
χ49222-22-2-2−1+i3−1−i3−1+i3−1−i3-11−i321+i321−i31+i3-11−i321+i3211−1+i32−1+i32−1−i32−1−i32000000-2-2-22-2221−i31+i31−i31+i31−1+i32−1−i32−1+i3−1−i31−1+i32−1−i32-1-11−i321−i321+i321+i32000000
χ502-220-20022-2-222200-2-2-2000000000000-22-20200-2-222-2-2-200222000000000000
χ512-220-20022-2-2-1-1-1001113−33−33−3000000-22-20200-2-22211100-1-1-1−33−33−33000000
χ522-220-20022-2-2-1-1-100111−33−33−33000000-22-20200-2-22211100-1-1-13−33−33−3000000
χ532-220-200−1−i3−1+i31+i31−i32−1−i3−1+i300-21+i31−i3000000000000-22-202001+i31−i3−1−i3−1+i3-21+i31−i3002−1−i3−1+i3000000000000
χ542-220-200−1−i3−1+i31+i31−i3-11+i321−i32001−1−i32−1+i323−32ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ11000000-22-202001+i31−i3−1−i3−1+i31−1−i32−1+i3200-11+i321−i32−33−2ζ7−ζ112ζ7+ζ11ζ7+2ζ11−ζ7−2ζ11000000
χ552-220-200−1−i3−1+i31+i31−i3-11+i321−i32001−1−i32−1+i32−33−2ζ7−ζ112ζ7+ζ11ζ7+2ζ11−ζ7−2ζ11000000-22-202001+i31−i3−1−i3−1+i31−1−i32−1+i3200-11+i321−i323−32ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ11000000
χ562-220-200−1+i3−1−i31−i31+i32−1+i3−1−i300-21−i31+i3000000000000-22-202001−i31+i3−1+i3−1−i3-21−i31+i3002−1+i3−1−i3000000000000
χ572-220-200−1+i3−1−i31−i31+i3-11−i321+i32001−1+i32−1−i323−3−ζ7−2ζ11ζ7+2ζ112ζ7+ζ11−2ζ7−ζ11000000-22-202001−i31+i3−1+i3−1−i31−1+i32−1−i3200-11−i321+i32−33ζ7+2ζ11−ζ7−2ζ11−2ζ7−ζ112ζ7+ζ11000000
χ582-220-200−1+i3−1−i31−i31+i3-11−i321+i32001−1+i32−1−i32−33ζ7+2ζ11−ζ7−2ζ11−2ζ7−ζ112ζ7+ζ11000000-22-202001−i31+i3−1+i3−1−i31−1+i32−1−i3200-11−i321+i323−3−ζ7−2ζ11ζ7+2ζ112ζ7+ζ11−2ζ7−ζ11000000
χ5966-36-3-3-3000000000000000000000000-6-63-6333000000000000000000000000
χ6066-3-6-333000000000000000000000000-6-6363-3-3000000000000000000000000
χ616-6-30333−33000000000000000000000000-6630-3−3333000000000000000000000000
χ626-6-303−3333000000000000000000000000-6630-333−33000000000000000000000000

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