Finite Group Databasebeta

← Group #67964

Character table — Group #67964

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51
size112444888888881616161124448888888816161611244488888888161616
order122444224488884483661212126612122424242412122436612121266121224242424121224
χ1111111111111111111111111111111111111111111111111111
χ21111111111-1-1-1-1-1-111111111111-1-1-1-1-1-111111111111-1-1-1-1-1-11
χ3111111-111-11111-1-1-1111111-111-11111-1-1-1111111-111-11111-1-1-1
χ4111111-111-1-1-1-1-111-1111111-111-1-1-1-1-111-1111111-111-1-1-1-1-111-1
χ51111-1-11-111ii−i−ii−i-11111-1-11-111ii−i−ii−i-11111-1-11-111ii−i−ii−i-1
χ61111-1-11-111−i−iii−ii-11111-1-11-111−i−iii−ii-11111-1-11-111−i−iii−ii-1
χ71111-1-1-1-11-1ii−i−i−ii11111-1-1-1-11-1ii−i−i−ii11111-1-1-1-11-1ii−i−i−ii1
χ81111-1-1-1-11-1−i−iiii−i11111-1-1-1-11-1−i−iiii−i11111-1-1-1-11-1−i−iiii−i1
χ92222220-2-2000000002222220-2-2000000002222220-2-200000000
χ102222-2-202-2000000002222-2-202-2000000002222-2-202-200000000
χ11444-40000000000000444-40000000000000444-40000000000000
χ1244-4000200-2000000044-4000200-2000000044-4000200-20000000
χ1344-4000-2002000000044-4000-2002000000044-4000-20020000000
χ144-4002i−2i00001+i−1−i1−i−1+i0004-4002i−2i00001+i−1−i1−i−1+i0004-4002i−2i00001+i−1−i1−i−1+i000
χ154-4002i−2i0000−1−i1+i−1+i1−i0004-4002i−2i0000−1−i1+i−1+i1−i0004-4002i−2i0000−1−i1+i−1+i1−i000
χ164-400−2i2i00001−i−1+i1+i−1−i0004-400−2i2i00001−i−1+i1+i−1−i0004-400−2i2i00001−i−1+i1+i−1−i000
χ174-400−2i2i0000−1+i1−i−1−i1+i0004-400−2i2i0000−1+i1−i−1−i1+i0004-400−2i2i0000−1+i1−i−1−i1+i000
χ1811111111111111111−1+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−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ191111111111-1-1-1-1-1-11−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32
χ20111111-111-11111-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32
χ21111111-111-1-1-1-1-111-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i321+i32
χ221111-1-11-111ii−i−ii−i-1−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i32−1+i32−1+i32ζ7ζ7−ζ7−ζ7ζ7−ζ71−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i32−1−i32ζ11ζ11−ζ11−ζ11ζ11−ζ111+i32
χ231111-1-11-111−i−iii−ii-1−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i32−1+i32−1+i32−ζ7−ζ7ζ7ζ7−ζ7ζ71−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i32−1−i32−ζ11−ζ11ζ11ζ11−ζ11ζ111+i32
χ241111-1-1-1-11-1ii−i−i−ii1−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i32ζ7ζ7−ζ7−ζ7−ζ7ζ7−1+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i32ζ11ζ11−ζ11−ζ11−ζ11ζ11−1−i32
χ251111-1-1-1-11-1−i−iiii−i1−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i32−ζ7−ζ7ζ7ζ7ζ7−ζ7−1+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i32−ζ11−ζ11ζ11ζ11ζ11−ζ11−1−i32
χ262222220-2-200000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i301−i31−i300000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i301+i31+i300000000
χ272222-2-202-200000000−1+i3−1+i3−1+i3−1+i31−i31−i30−1+i31−i300000000−1−i3−1−i3−1−i3−1−i31+i31+i30−1−i31+i300000000
χ28444-40000000000000−2+2i3−2+2i3−2+2i32−2i30000000000000−2−2i3−2−2i3−2−2i32+2i30000000000000
χ2944-4000200-20000000−2+2i3−2+2i32−2i3000−1+i3001−i30000000−2−2i3−2−2i32+2i3000−1−i3001+i30000000
χ3044-4000-20020000000−2+2i3−2+2i32−2i30001−i300−1+i30000000−2−2i3−2−2i32+2i30001+i300−1−i30000000
χ314-4002i−2i00001+i−1−i1−i−1+i000−2+2i32−2i3002ζ7−2ζ70000ζ7−ζ10−ζ7+ζ10−ζ7−ζ10ζ7+ζ10000−2−2i32+2i3002ζ11−2ζ110000−ζ2+ζ11ζ2−ζ11−ζ2−ζ11ζ2+ζ11000
χ324-4002i−2i0000−1−i1+i−1+i1−i000−2+2i32−2i3002ζ7−2ζ70000−ζ7+ζ10ζ7−ζ10ζ7+ζ10−ζ7−ζ10000−2−2i32+2i3002ζ11−2ζ110000ζ2−ζ11−ζ2+ζ11ζ2+ζ11−ζ2−ζ11000
χ334-400−2i2i00001−i−1+i1+i−1−i000−2+2i32−2i300−2ζ72ζ70000−ζ7−ζ10ζ7+ζ10ζ7−ζ10−ζ7+ζ10000−2−2i32+2i300−2ζ112ζ110000−ζ2−ζ11ζ2+ζ11−ζ2+ζ11ζ2−ζ11000
χ344-400−2i2i0000−1+i1−i−1−i1+i000−2+2i32−2i300−2ζ72ζ70000ζ7+ζ10−ζ7−ζ10−ζ7+ζ10ζ7−ζ10000−2−2i32+2i300−2ζ112ζ110000ζ2+ζ11−ζ2−ζ11ζ2−ζ11−ζ2+ζ11000
χ3511111111111111111−1−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+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ361111111111-1-1-1-1-1-11−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32
χ37111111-111-11111-1-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32
χ38111111-111-1-1-1-1-111-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i321−i32
χ391111-1-11-111ii−i−ii−i-1−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i32−1−i32ζ11ζ11−ζ11−ζ11ζ11−ζ111+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i32−1+i32−1+i32ζ7ζ7−ζ7−ζ7ζ7−ζ71−i32
χ401111-1-11-111−i−iii−ii-1−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i32−1−i32−ζ11−ζ11ζ11ζ11−ζ11ζ111+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i32−1+i32−1+i32−ζ7−ζ7ζ7ζ7−ζ7ζ71−i32
χ411111-1-1-1-11-1ii−i−i−ii1−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i32ζ11ζ11−ζ11−ζ11−ζ11ζ11−1−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i32ζ7ζ7−ζ7−ζ7−ζ7ζ7−1+i32
χ421111-1-1-1-11-1−i−iiii−i1−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i32−ζ11−ζ11ζ11ζ11ζ11−ζ11−1−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i32−ζ7−ζ7ζ7ζ7ζ7−ζ7−1+i32
χ432222220-2-200000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i301+i31+i300000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i301−i31−i300000000
χ442222-2-202-200000000−1−i3−1−i3−1−i3−1−i31+i31+i30−1−i31+i300000000−1+i3−1+i3−1+i3−1+i31−i31−i30−1+i31−i300000000
χ45444-40000000000000−2−2i3−2−2i3−2−2i32+2i30000000000000−2+2i3−2+2i3−2+2i32−2i30000000000000
χ4644-4000200-20000000−2−2i3−2−2i32+2i3000−1−i3001+i30000000−2+2i3−2+2i32−2i3000−1+i3001−i30000000
χ4744-4000-20020000000−2−2i3−2−2i32+2i30001+i300−1−i30000000−2+2i3−2+2i32−2i30001−i300−1+i30000000
χ484-4002i−2i00001+i−1−i1−i−1+i000−2−2i32+2i3002ζ11−2ζ110000−ζ2+ζ11ζ2−ζ11−ζ2−ζ11ζ2+ζ11000−2+2i32−2i3002ζ7−2ζ70000ζ7−ζ10−ζ7+ζ10−ζ7−ζ10ζ7+ζ10000
χ494-4002i−2i0000−1−i1+i−1+i1−i000−2−2i32+2i3002ζ11−2ζ110000ζ2−ζ11−ζ2+ζ11ζ2+ζ11−ζ2−ζ11000−2+2i32−2i3002ζ7−2ζ70000−ζ7+ζ10ζ7−ζ10ζ7+ζ10−ζ7−ζ10000
χ504-400−2i2i00001−i−1+i1+i−1−i000−2−2i32+2i300−2ζ112ζ110000−ζ2−ζ11ζ2+ζ11−ζ2+ζ11ζ2−ζ11000−2+2i32−2i300−2ζ72ζ70000−ζ7−ζ10ζ7+ζ10ζ7−ζ10−ζ7+ζ10000
χ514-400−2i2i0000−1+i1−i−1−i1+i000−2−2i32+2i300−2ζ112ζ110000ζ2+ζ11−ζ2−ζ11ζ2−ζ11−ζ2+ζ11000−2+2i32−2i300−2ζ72ζ70000ζ7+ζ10−ζ7−ζ10−ζ7+ζ10ζ7−ζ10000

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