Finite Group Databasebeta

← Group #72258712

Character table — Group #72258712

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76
size111122333344666666666688881212121212121212121212121212161616161616161616162424242432323232323232323232323248486464646464646464
order1222442222244444444444224424444444444444233466666644446666121212121212121244666612121212
χ11111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111−1−i32−1+i321−1−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+i32−1+i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ311111111111111111111111111111111111111111−1+i32−1−i321−1+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−i32−1−i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ41111111111111111111111-1-1-1-111111111111111-111-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11-11-11-11-1
χ51111111111111111111111-1-1-1-111111111111111-1−1−i32−1+i32-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-11+i321+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32-1-1−1−i321+i32−1+i321−i32−1−i321+i32−1+i321−i32
χ61111111111111111111111-1-1-1-111111111111111-1−1+i32−1−i32-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-11−i321−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32-1-1−1+i321−i32−1−i321+i32−1+i321−i32−1−i321+i32
χ71111111111-1-111111111111111-1-11111-1-1-1-1-1-1-1-1-111-11111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ81111111111-1-111111111111111-1-11111-1-1-1-1-1-1-1-1-1−1−i32−1+i32-1−1−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+i32−1+i32−1+i32−1+i32-1-11+i321+i321−i321−i321+i321+i321−i321−i32
χ91111111111-1-111111111111111-1-11111-1-1-1-1-1-1-1-1-1−1+i32−1−i32-1−1+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−i32−1−i32−1−i32−1−i32-1-11−i321−i321+i321+i321−i321−i321+i321+i32
χ101111111111-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-111-11-11-11-11
χ111111111111-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11−1−i32−1+i321−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-11+i321+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32111+i32−1−i321−i32−1+i321+i32−1−i321−i32−1+i32
χ121111111111-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11−1+i32−1−i321−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-11−i321−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32111−i32−1+i321+i32−1−i321−i32−1+i321+i32−1−i32
χ131111-1-111111-1-1-11111111111-1-11-1-1-1-1-1-1-1-1-11111-1111111111-1-1111111-1-1-1-1-1-1-1-11-11-11-1-11-11
χ141111-1-111111-1-1-11111111111-1-11-1-1-1-1-1-1-1-1-11111-1−1−i32−1+i321−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-111−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i321-1−1−i321+i32−1+i321−i321+i32−1−i321−i32−1+i32
χ151111-1-111111-1-1-11111111111-1-11-1-1-1-1-1-1-1-1-11111-1−1+i32−1−i321−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-111−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i321-1−1+i321−i32−1−i321+i321−i32−1+i321+i32−1−i32
χ161111-1-111111-1-1-111111111-1-1111-1-1-1-1-1-1-1-1-11111111-111111111-1-1-1-1-1-1-1-111-1-111-111111-1-1-1-1
χ171111-1-111111-1-1-111111111-1-1111-1-1-1-1-1-1-1-1-111111−1−i32−1+i32-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211-1-11+i321+i321−i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-11−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32
χ181111-1-111111-1-1-111111111-1-1111-1-1-1-1-1-1-1-1-111111−1+i32−1−i32-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211-1-11−i321−i321+i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-11−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32
χ191111-1-11111-11-1-11111111111-1-1-11-1-1-1-11111-1-1-1-1111-1111111-1-1111111-1-1-1-1-1-1-1-1-11-11-111-11-1
χ201111-1-11111-11-1-11111111111-1-1-11-1-1-1-11111-1-1-1-11−1−i32−1+i32-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-111−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32-111+i32−1−i321−i32−1+i32−1−i321+i32−1+i321−i32
χ211111-1-11111-11-1-11111111111-1-1-11-1-1-1-11111-1-1-1-11−1+i32−1−i32-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-111−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32-111−i32−1+i321+i32−1−i32−1+i321−i32−1−i321+i32
χ221111-1-11111-11-1-111111111-1-111-11-1-1-1-11111-1-1-1-1-111111111111-1-1-1-1-1-1-1-111-1-1111-1-1-1-1-11111
χ231111-1-11111-11-1-111111111-1-111-11-1-1-1-11111-1-1-1-1-1−1−i32−1+i321−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211-1-11+i321+i321−i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321-11+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32
χ241111-1-11111-11-1-111111111-1-111-11-1-1-1-11111-1-1-1-1-1−1+i32−1−i321−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211-1-11−i321−i321+i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321-11−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32
χ2522-2-22i−2i2-2-22002i−2i2222-2-2-2-20000002i2i−2i−2i00000000022022-2-2-2-2000000002i−2i002i−2i000000000000
χ2622-2-22i−2i2-2-22002i−2i2222-2-2-2-20000002i2i−2i−2i000000000−1−i3−1+i30−1−i3−1+i31+i31+i31−i31−i3000000002ζ11−2ζ11002ζ7−2ζ7000000000000
χ2722-2-22i−2i2-2-22002i−2i2222-2-2-2-20000002i2i−2i−2i000000000−1+i3−1−i30−1+i3−1−i31−i31−i31+i31+i3000000002ζ7−2ζ7002ζ11−2ζ11000000000000
χ2822-2-2−2i2i2-2-2200−2i2i2222-2-2-2-2000000−2i−2i2i2i00000000022022-2-2-2-200000000−2i2i00−2i2i000000000000
χ2922-2-2−2i2i2-2-2200−2i2i2222-2-2-2-2000000−2i−2i2i2i000000000−1−i3−1+i30−1−i3−1+i31+i31+i31−i31−i300000000−2ζ112ζ1100−2ζ72ζ7000000000000
χ3022-2-2−2i2i2-2-2200−2i2i2222-2-2-2-2000000−2i−2i2i2i000000000−1+i3−1−i30−1+i3−1−i31−i31−i31+i31+i300000000−2ζ72ζ700−2ζ112ζ11000000000000
χ312-22-200-22-22000022-2-222-2-2002-2000000000000000220-2-22-22-22-2000000002-2002-20000000000
χ322-22-200-22-22000022-2-222-2-2002-2000000000000000−1−i3−1+i301+i31−i3−1−i31+i3−1+i31−i32-200000000−1−i31+i300−1+i31−i30000000000
χ332-22-200-22-22000022-2-222-2-2002-2000000000000000−1+i3−1−i301−i31+i3−1+i31−i3−1−i31+i32-200000000−1+i31−i300−1−i31+i30000000000
χ342-22-200-22-22000022-2-222-2-200-22000000000000000220-2-22-22-2-2200000000-2200-220000000000
χ352-22-200-22-22000022-2-222-2-200-22000000000000000−1−i3−1+i301+i31−i3−1−i31+i3−1+i31−i3-22000000001+i3−1−i3001−i3−1+i30000000000
χ362-22-200-22-22000022-2-222-2-200-22000000000000000−1+i3−1−i301−i31+i3−1+i31−i3−1−i31+i3-22000000001−i3−1+i3001+i3−1−i30000000000
χ372-2-2200-2-222000022-2-2-2-2222-200000000000000000220-2-2-22-22002-22-22-2000000000000000000
χ382-2-2200-2-222000022-2-2-2-2222-200000000000000000−1−i3−1+i301+i31−i31+i3−1−i31−i3−1+i3002-2−1−i31+i3−1+i31−i3000000000000000000
χ392-2-2200-2-222000022-2-2-2-2222-200000000000000000−1+i3−1−i301−i31+i31−i3−1+i31+i3−1−i3002-2−1+i31−i3−1−i31+i3000000000000000000
χ402-2-2200-2-222000022-2-2-2-222-2200000000000000000220-2-2-22-2200-22-22-22000000000000000000
χ412-2-2200-2-222000022-2-2-2-222-2200000000000000000−1−i3−1+i301+i31−i31+i3−1−i31−i3−1+i300-221+i3−1−i31−i3−1+i3000000000000000000
χ422-2-2200-2-222000022-2-2-2-222-2200000000000000000−1+i3−1−i301−i31+i31−i3−1+i31+i3−1−i300-221−i3−1+i31+i3−1−i3000000000000000000
χ4333333333333333-1-1-1-1-1-1-1-1333333-1-1-1-1-1-1-1-1-1-1-1-13003000000-1-1-1-1000000000000-1-100000000
χ4433333333333333-1-1-1-1-1-1-1-1-3-3-3-333-1-1-1-1-1-1-1-1-1-1-1-1-300-300000011110000000000001100000000
χ453333333333-3-333-1-1-1-1-1-1-1-13333-3-3-1-1-1-111111111-300-3000000-1-1-1-10000000000001100000000
χ463333333333-3-333-1-1-1-1-1-1-1-1-3-3-3-3-3-3-1-1-1-11111111130030000001111000000000000-1-100000000
χ473333-3-333333-3-3-3-1-1-1-1-1-1-1-133-3-33-311111111-1-1-1-1-300300000011-1-1000000000000-1100000000
χ483333-3-333333-3-3-3-1-1-1-1-1-1-1-1-3-3333-311111111-1-1-1-1300-3000000-1-1110000000000001-100000000
χ493333-3-33333-33-3-3-1-1-1-1-1-1-1-133-3-3-331111-1-1-1-11111300-300000011-1-10000000000001-100000000
χ503333-3-33333-33-3-3-1-1-1-1-1-1-1-1-3-333-331111-1-1-1-11111-3003000000-1-111000000000000-1100000000
χ51666666-2-2-2-266-2-22i−2i2i−2i2i−2i2i−2i0000-2-22i−2i2i−2i2i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000
χ52666666-2-2-2-266-2-2−2i2i−2i2i−2i2i−2i2i0000-2-2−2i2i−2i2i−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000
χ53666666-2-2-2-2-6-6-2-22i−2i2i−2i2i−2i2i−2i0000222i−2i2i−2i−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000
χ54666666-2-2-2-2-6-6-2-2−2i2i−2i2i−2i2i−2i2i000022−2i2i−2i2i2i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000
χ556666-6-6-2-2-2-26-6222i−2i2i−2i2i−2i2i−2i0000-22−2i2i−2i2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
χ566666-6-6-2-2-2-26-622−2i2i−2i2i−2i2i−2i2i0000-222i−2i2i−2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ576666-6-6-2-2-2-2-66222i−2i2i−2i2i−2i2i−2i00002-2−2i2i−2i2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ586666-6-6-2-2-2-2-6622−2i2i−2i2i−2i2i−2i2i00002-22i−2i2i−2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
χ5966-6-66i−6i6-6-66006i−6i-2-2-2-22222000000−2i−2i2i2i00000000000000000000000000000000000000000000
χ6066-6-66i−6i-222-200−2i2i2i−2i2i−2i−2i2i−2i2i000000-222-22+2i−2−2i2−2i−2+2i2−2i−2+2i2+2i−2−2i000000000000000000000000000000000000
χ6166-6-66i−6i-222-200−2i2i2i−2i2i−2i−2i2i−2i2i000000-222-2−2−2i2+2i−2+2i2−2i−2+2i2−2i−2−2i2+2i000000000000000000000000000000000000
χ6266-6-66i−6i-222-200−2i2i−2i2i−2i2i2i−2i2i−2i0000002-2-222−2i−2+2i2+2i−2−2i−2−2i2+2i−2+2i2−2i000000000000000000000000000000000000
χ6366-6-66i−6i-222-200−2i2i−2i2i−2i2i2i−2i2i−2i0000002-2-22−2+2i2−2i−2−2i2+2i2+2i−2−2i2−2i−2+2i000000000000000000000000000000000000
χ6466-6-6−6i6i6-6-6600−6i6i-2-2-2-222220000002i2i−2i−2i00000000000000000000000000000000000000000000
χ6566-6-6−6i6i-222-2002i−2i2i−2i2i−2i−2i2i−2i2i0000002-2-222+2i−2−2i2−2i−2+2i−2+2i2−2i−2−2i2+2i000000000000000000000000000000000000
χ6666-6-6−6i6i-222-2002i−2i2i−2i2i−2i−2i2i−2i2i0000002-2-22−2−2i2+2i−2+2i2−2i2−2i−2+2i2+2i−2−2i000000000000000000000000000000000000
χ6766-6-6−6i6i-222-2002i−2i−2i2i−2i2i2i−2i2i−2i000000-222-22−2i−2+2i2+2i−2−2i2+2i−2−2i2−2i−2+2i000000000000000000000000000000000000
χ6866-6-6−6i6i-222-2002i−2i−2i2i−2i2i2i−2i2i−2i000000-222-2−2+2i2−2i−2−2i2+2i−2−2i2+2i−2+2i2−2i000000000000000000000000000000000000
χ696-66-600-66-660000-2-222-2-222006-6000000000000000000000000-22000000000000000000000000
χ706-66-600-66-660000-2-222-2-22200-660000000000000000000000002-2000000000000000000000000
χ716-6-6600-6-6660000-2-22222-2-26-60000000000000000000000000000-220000000000000000000000
χ726-6-6600-6-6660000-2-22222-2-2-6600000000000000000000000000002-20000000000000000000000
χ7312-1212-12004-44-400004i−4i−4i4i4i−4i−4i4i000000000000000000000000000000000000000000000000000000
χ7412-1212-12004-44-40000−4i4i4i−4i−4i4i4i−4i000000000000000000000000000000000000000000000000000000
χ7512-12-12120044-4-400004i−4i−4i4i−4i4i4i−4i000000000000000000000000000000000000000000000000000000
χ7612-12-12120044-4-40000−4i4i4i−4i4i−4i−4i4i000000000000000000000000000000000000000000000000000000

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