Finite Group Databasebeta

← Group #72222714

Character table — Group #72222714

Order 2304.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size113344444461212121212121212161616161616161616161616182436364848484848484848646464646464646464646464646464647296969696
order1222223366444446666336666666666444412121212121212123333666666666666412121212
χ11111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111−1−i32−1+i321111−1−i32−1−i32−1+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+i32−1+i32−1+i32−1+i32−1+i32−1+i321−1−i32−1−i32−1+i32−1+i32
χ31111111111111111111−1+i32−1−i321111−1+i32−1+i32−1−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−i32−1−i32−1−i32−1−i32−1−i32−1−i321−1+i32−1+i32−1−i32−1−i32
χ4111111−1−i32−1+i32−1−i32−1+i3211111−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321111111111−1−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+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211111
χ5111111−1−i32−1+i32−1−i32−1+i3211111−1−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+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i3211−1−i32−1+i32−1+i32−1+i32111111−1−i32−1−i32−1−i321−1−i32−1−i32−1+i32−1+i32
χ6111111−1−i32−1+i32−1−i32−1+i3211111−1−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−i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321−1−i32−1+i321111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321111−1+i32−1+i32−1−i32−1−i32
χ7111111−1+i32−1−i32−1+i32−1−i3211111−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321111111111−1+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−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211111
χ8111111−1+i32−1−i32−1+i32−1−i3211111−1+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+i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−1+i32−1−i321111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321111−1−i32−1−i32−1+i32−1+i32
χ9111111−1+i32−1−i32−1+i32−1−i3211111−1+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−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i3211−1+i32−1−i32−1−i32−1−i32111111−1+i32−1+i32−1+i321−1+i32−1+i32−1−i32−1−i32
χ101111-1-11111111-1-1111111-1-1-1-1-1-1-1-1111-11111-1-111-1-111111-1-11-1-11-1-11-1-1-11-11-1
χ111111-1-11111111-1-11111−1−i32−1+i32-1-1-1-11+i321+i321−i321−i32−1−i32−1+i321-11111-1-111-1-1−1−i32−1−i32−1+i32−1+i32−1−i321+i321+i32−1−i321+i321+i32−1+i321−i321−i32−1+i321−i321−i32-1−1−i321+i32−1+i321−i32
χ121111-1-11111111-1-11111−1+i32−1−i32-1-1-1-11−i321−i321+i321+i32−1+i32−1−i321-11111-1-111-1-1−1+i32−1+i32−1−i32−1−i32−1+i321−i321−i32−1+i321−i321−i32−1−i321+i321+i32−1−i321+i321+i32-1−1+i321−i32−1−i321+i32
χ131111-1-1−1−i32−1+i32−1−i32−1+i32111-1-1−1−i32−1+i32−1−i32−1+i32111+i321+i321−i321−i32-1-1-1-1111-111−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1+i32−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i32−1−i321+i321+i32−1+i321−i321−i32-11-11-1
χ141111-1-1−1−i32−1+i32−1−i32−1+i32111-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i32−1−i32−1+i321-111−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1+i3211−1−i32−1+i321−i321−i321-1-11-1-1−1−i321+i321+i32-1−1−i321+i32−1+i321−i32
χ151111-1-1−1−i32−1+i32−1−i32−1+i32111-1-1−1−i32−1+i32−1−i32−1+i32−1+i32−1−i321+i321+i321−i321−i321−i321−i321+i321+i32−1+i32−1−i321-111−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321−1−i32−1+i3211-1-1−1−i321+i321+i32−1+i321−i321−i321-1-1-1−1+i321−i32−1−i321+i32
χ161111-1-1−1+i32−1−i32−1+i32−1−i32111-1-1−1+i32−1−i32−1+i32−1−i32111−i321−i321+i321+i32-1-1-1-1111-111−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1−i32−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32−1+i321−i321−i32−1−i321+i321+i32-11-11-1
χ171111-1-1−1+i32−1−i32−1+i32−1−i32111-1-1−1+i32−1−i32−1+i32−1−i32−1−i32−1+i321−i321−i321+i321+i321+i321+i321−i321−i32−1−i32−1+i321-111−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321−1+i32−1−i3211-1-1−1+i321−i321−i32−1−i321+i321+i321-1-1-1−1−i321+i32−1+i321−i32
χ181111-1-1−1+i32−1−i32−1+i32−1−i32111-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i32−1+i32−1−i321-111−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1−i3211−1+i32−1−i321+i321+i321-1-11-1-1−1+i321−i321−i32-1−1+i321−i32−1−i321+i32
χ193333330000-133330000330000333333-1-1-1-1000000000000000000000000-1-1-1-1-1
χ203333330000-133330000−3−3i32−3+3i320000−3−3i32−3−3i32−3+3i32−3+3i32−3−3i32−3+3i32-1-1-1-1000000000000000000000000-11+i321+i321−i321−i32
χ213333330000-133330000−3+3i32−3−3i320000−3+3i32−3+3i32−3−3i32−3−3i32−3+3i32−3−3i32-1-1-1-1000000000000000000000000-11−i321−i321+i321+i32
χ2233333333333-1-1-1-1333300333300000033-1-1-1-1-1-1-1-1-1-10000000000000000-10000
χ23333333−3−3i32−3+3i32−3−3i32−3+3i323-1-1-1-1−3−3i32−3+3i32−3−3i32−3+3i3200−3−3i32−3−3i32−3+3i32−3+3i3200000033-1-11+i321+i321+i321+i321−i321−i321−i321−i320000000000000000-10000
χ24333333−3+3i32−3−3i32−3+3i32−3−3i323-1-1-1-1−3+3i32−3−3i32−3+3i32−3−3i3200−3+3i32−3+3i32−3−3i32−3−3i3200000033-1-11−i321−i321−i321−i321+i321+i321+i321+i320000000000000000-10000
χ253333-3-30000-133-3-30000330000-3-3-3-333-11-1-10000000000000000000000001-11-11
χ263333-3-30000-133-3-30000−3−3i32−3+3i3200003+3i323+3i323−3i323−3i32−3−3i32−3+3i32-11-1-100000000000000000000000011+i32−1−i321−i32−1+i32
χ273333-3-30000-133-3-30000−3+3i32−3−3i3200003−3i323−3i323+3i323+3i32−3+3i32−3−3i32-11-1-100000000000000000000000011−i32−1+i321+i32−1−i32
χ283333-3-333333-1-111333300-3-3-3-30000003-3-1-1-1-111-1-111000000000000000010000
χ293333-3-3−3−3i32−3+3i32−3−3i32−3+3i323-1-111−3−3i32−3+3i32−3−3i32−3+3i32003+3i323+3i323−3i323−3i320000003-3-1-11+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32000000000000000010000
χ303333-3-3−3+3i32−3−3i32−3+3i32−3−3i323-1-111−3+3i32−3−3i32−3+3i32−3−3i32003−3i323−3i323+3i323+3i320000003-3-1-11−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32000000000000000010000
χ314-4-444-4-2-22200000-2-222-2-22-22-22-22-2220000000000001111-11-1-11-1-11-1-11-100000
χ324-4-444-4-2-22200000-2-2221+i31−i32-22-2−1−i31+i3−1+i31−i3−1−i3−1+i3000000000000−1−i32−1−i32−1+i32−1+i321+i32−1−i321+i321+i32−1−i321+i321−i32−1+i321−i321−i32−1+i321−i3200000
χ334-4-444-4-2-22200000-2-2221−i31+i32-22-2−1+i31−i3−1−i31+i3−1+i3−1−i3000000000000−1+i32−1+i32−1−i32−1−i321−i32−1+i321−i321−i32−1+i321−i321+i32−1−i321+i321+i32−1−i321+i3200000
χ344-4-444-41+i31−i3−1−i3−1+i3000001+i31−i3−1−i3−1+i3-2-2−1−i31+i3−1+i31−i32-22-222000000000000−1−i32−1+i32−1−i32−1+i321+i32−1−i321+i321−i32−1+i321−i321+i32−1−i321+i321−i32−1+i321−i3200000
χ354-4-444-41+i31−i3−1−i3−1+i3000001+i31−i3−1−i3−1+i31+i31−i3−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i3−1−i3−1+i3000000000000−1+i3211−1−i321−i32−1+i321−i32-11-1-11-11+i32−1−i321+i3200000
χ364-4-444-41+i31−i3−1−i3−1+i3000001+i31−i3−1−i3−1+i31−i31+i3−1−i31+i3−1+i31−i3−1+i31−i3−1−i31+i3−1+i3−1−i30000000000001−1−i32−1+i321-11-11+i32−1−i321+i321−i32−1+i321−i32-11-100000
χ374-4-444-41−i31+i3−1+i3−1−i3000001−i31+i3−1+i3−1−i3-2-2−1+i31−i3−1−i31+i32-22-222000000000000−1+i32−1−i32−1+i32−1−i321−i32−1+i321−i321+i32−1−i321+i321−i32−1+i321−i321+i32−1−i321+i3200000
χ384-4-444-41−i31+i3−1+i3−1−i3000001−i31+i3−1+i3−1−i31+i31−i3−1+i31−i3−1−i31+i3−1−i31+i3−1+i31−i3−1−i3−1+i30000000000001−1+i32−1−i321-11-11−i32−1+i321−i321+i32−1−i321+i32-11-100000
χ394-4-444-41−i31+i3−1+i3−1−i3000001−i31+i3−1+i3−1−i31−i31+i3−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i3−1+i3−1−i3000000000000−1−i3211−1+i321+i32−1−i321+i32-11-1-11-11−i32−1+i321−i3200000
χ404-4-44-44-2-22200000-2-222-2-2-22-22-22-22220000000000001111-1-11-1-11-1-11-1-1100000
χ414-4-44-44-2-22200000-2-2221+i31−i3-22-221+i3−1−i31−i3−1+i3−1−i3−1+i3000000000000−1−i32−1−i32−1+i32−1+i321+i321+i32−1−i321+i321+i32−1−i321−i321−i32−1+i321−i321−i32−1+i3200000
χ424-4-44-44-2-22200000-2-2221−i31+i3-22-221−i3−1+i31+i3−1−i3−1+i3−1−i3000000000000−1+i32−1+i32−1−i32−1−i321−i321−i32−1+i321−i321−i32−1+i321+i321+i32−1−i321+i321+i32−1−i3200000
χ434-4-44-441+i31−i3−1−i3−1+i3000001+i31−i3−1−i3−1+i3-2-21+i3−1−i31−i3−1+i3-22-2222000000000000−1−i32−1+i32−1−i32−1+i321+i321+i32−1−i321−i321−i32−1+i321+i321+i32−1−i321−i321−i32−1+i3200000
χ444-4-44-441+i31−i3−1−i3−1+i3000001+i31−i3−1−i3−1+i31+i31−i31+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i3−1−i3−1+i3000000000000−1+i3211−1−i321−i321−i32−1+i32-1-11-1-111+i321+i32−1−i3200000
χ454-4-44-441+i31−i3−1−i3−1+i3000001+i31−i3−1−i3−1+i31−i31+i31+i3−1−i31−i3−1+i31−i3−1+i31+i3−1−i3−1+i3−1−i30000000000001−1−i32−1+i321-1-111+i321+i32−1−i321−i321−i32−1+i32-1-1100000
χ464-4-44-441−i31+i3−1+i3−1−i3000001−i31+i3−1+i3−1−i3-2-21−i3−1+i31+i3−1−i3-22-2222000000000000−1+i32−1−i32−1+i32−1−i321−i321−i32−1+i321+i321+i32−1−i321−i321−i32−1+i321+i321+i32−1−i3200000
χ474-4-44-441−i31+i3−1+i3−1−i3000001−i31+i3−1+i3−1−i31+i31−i31−i3−1+i31+i3−1−i31+i3−1−i31−i3−1+i3−1−i3−1+i30000000000001−1+i32−1−i321-1-111−i321−i32−1+i321+i321+i32−1−i32-1-1100000
χ484-4-44-441−i31+i3−1+i3−1−i3000001−i31+i3−1+i3−1−i31−i31+i31−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i3−1+i3−1−i3000000000000−1−i3211−1+i321+i321+i32−1−i32-1-11-1-111−i321−i32−1+i3200000
χ4966-2-200666662i−2i00-2-2-2-2000000000000-202i−2i2i−2i002i−2i00000000000000000000000
χ5066-2-20066666−2i2i00-2-2-2-2000000000000-20−2i2i−2i2i00−2i2i00000000000000000000000
χ5166-2-200−3−3i3−3+3i3−3−3i3−3+3i362i−2i001+i31−i31+i31−i3000000000000-202i−2i2ζ11−2ζ11002ζ7−2ζ700000000000000000000000
χ5266-2-200−3−3i3−3+3i3−3−3i3−3+3i36−2i2i001+i31−i31+i31−i3000000000000-20−2i2i−2ζ112ζ1100−2ζ72ζ700000000000000000000000
χ5366-2-200−3+3i3−3−3i3−3+3i3−3−3i362i−2i001−i31+i31−i31+i3000000000000-202i−2i2ζ7−2ζ7002ζ11−2ζ1100000000000000000000000
χ5466-2-200−3+3i3−3−3i3−3+3i3−3−3i36−2i2i001−i31+i31−i31+i3000000000000-20−2i2i−2ζ72ζ700−2ζ112ζ1100000000000000000000000
χ559999990000-3-3-3-3-30000000000000000-3-31100000000000000000000000010000
χ569999-9-90000-3-3-3330000000000000000-3311000000000000000000000000-10000
χ5712-124-400-6-6660004-422-2-20000000000000000002-2002-2000000000000000000000
χ5812-124-400-6-666000-4422-2-2000000000000000000-2200-22000000000000000000000
χ5912-124-4003+3i33−3i3−3−3i3−3+3i30004-4−1−i3−1+i31+i31−i3000000000000000000−1−i31+i300−1+i31−i3000000000000000000000
χ6012-124-4003+3i33−3i3−3−3i3−3+3i3000-44−1−i3−1+i31+i31−i30000000000000000001+i3−1−i3001−i3−1+i3000000000000000000000
χ6112-124-4003−3i33+3i3−3+3i3−3−3i30004-4−1+i3−1−i31−i31+i3000000000000000000−1+i31−i300−1−i31+i3000000000000000000000
χ6212-124-4003−3i33+3i3−3+3i3−3−3i3000-44−1+i3−1−i31−i31+i30000000000000000001−i3−1+i3001+i3−1−i3000000000000000000000
χ631818-6-6000000-66i−6i00000000000000000020−2i2i00000000000000000000000000000
χ641818-6-6000000-6−6i6i000000000000000000202i−2i00000000000000000000000000000

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