Finite Group Databasebeta

← Group #11920121

Character table — Group #11920121

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size113344121224242424242424242432323232113344121224242424242424242432323232113344121224242424242424242432323232
order1222442244444888836121236661212661212121212242424243612123666121266121212121224242424361212
χ1111111111111111111111111111111111111111111111111111111111111111
χ2111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-11111
χ31111-1-1-1-11ii−i−iii−i−i11-1-11111-1-1-1-11ii−i−iii−i−i11-1-11111-1-1-1-11ii−i−iii−i−i11-1-1
χ41111-1-1-1-11−i−iii−i−iii11-1-11111-1-1-1-11−i−iii−i−iii11-1-11111-1-1-1-11−i−iii−i−iii11-1-1
χ522222222200000000-1-1-1-122222222200000000-1-1-1-122222222200000000-1-1-1-1
χ62222-2-2-2-2200000000-1-1112222-2-2-2-2200000000-1-1112222-2-2-2-2200000000-1-111
χ72-22-22i−2i0001+i−1−i1−i−1+i0000-11i−i2-22-22i−2i0001+i−1−i1−i−1+i0000-11i−i2-22-22i−2i0001+i−1−i1−i−1+i0000-11i−i
χ82-22-22i−2i000−1−i1+i−1+i1−i0000-11i−i2-22-22i−2i000−1−i1+i−1+i1−i0000-11i−i2-22-22i−2i000−1−i1+i−1+i1−i0000-11i−i
χ92-22-2−2i2i0001−i−1+i1+i−1−i0000-11−ii2-22-2−2i2i0001−i−1+i1+i−1−i0000-11−ii2-22-2−2i2i0001−i−1+i1+i−1−i0000-11−ii
χ102-22-2−2i2i000−1+i1−i−1−i1+i0000-11−ii2-22-2−2i2i000−1+i1−i−1−i1+i0000-11−ii2-22-2−2i2i000−1+i1−i−1−i1+i0000-11−ii
χ11333333-1-1-11111-1-1-1-10000333333-1-1-11111-1-1-1-10000333333-1-1-11111-1-1-1-10000
χ12333333-1-1-1-1-1-1-111110000333333-1-1-1-1-1-1-111110000333333-1-1-1-1-1-1-111110000
χ133333-3-311-1ii−i−i−i−iii00003333-3-311-1ii−i−i−i−iii00003333-3-311-1ii−i−i−i−iii0000
χ143333-3-311-1−i−iiiii−i−i00003333-3-311-1−i−iiiii−i−i00003333-3-311-1−i−iiiii−i−i0000
χ154-44-44i−4i000000000001-1−ii4-44-44i−4i000000000001-1−ii4-44-44i−4i000000000001-1−ii
χ164-44-4−4i4i000000000001-1i−i4-44-4−4i4i000000000001-1i−i4-44-4−4i4i000000000001-1i−i
χ176-6-22002-200000i2−i2i2−i200006-6-22002-200000i2−i2i2−i200006-6-22002-200000i2−i2i2−i20000
χ186-6-22002-200000−i2i2−i2i200006-6-22002-200000−i2i2−i2i200006-6-22002-200000−i2i2−i2i20000
χ196-6-2200-22000002−2−2200006-6-2200-22000002−2−2200006-6-2200-22000002−2−220000
χ206-6-2200-2200000−222−200006-6-2200-2200000−222−200006-6-2200-2200000−222−20000
χ211212-4-4000000000000000001212-4-4000000000000000001212-4-400000000000000000
χ22111111111111111111111−1+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−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ23111111111-1-1-1-1-1-1-1-11111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−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−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32
χ241111-1-1-1-11ii−i−iii−i−i11-1-1−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32ζ14ζ14−ζ14−ζ14ζ14ζ14−ζ14−ζ14−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32ζ22ζ22−ζ22−ζ22ζ22ζ22−ζ22−ζ22−1−i32−1−i321+i321+i32
χ251111-1-1-1-11−i−iii−i−iii11-1-1−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−ζ14−ζ14ζ14ζ14−ζ14−ζ14ζ14ζ14−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−ζ22−ζ22ζ22ζ22−ζ22−ζ22ζ22ζ22−1−i32−1−i321+i321+i32
χ2622222222200000000-1-1-1-1−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3000000001−i321−i321−i321−i32−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3000000001+i321+i321+i321+i32
χ272222-2-2-2-2200000000-1-111−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i3−1+i3000000001−i321−i32−1+i32−1+i32−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i3−1−i3000000001+i321+i32−1−i32−1−i32
χ282-22-22i−2i0001+i−1−i1−i−1+i0000-11i−i−1+i31−i3−1+i31−i32ζ14−2ζ14000ζ14−ζ20−ζ14+ζ20−ζ14−ζ20ζ14+ζ2000001−i32−1+i32ζ14−ζ14−1−i31+i3−1−i31+i32ζ22−2ζ22000−ζ4+ζ22ζ4−ζ22−ζ4−ζ22ζ4+ζ2200001+i32−1−i32ζ22−ζ22
χ292-22-22i−2i000−1−i1+i−1+i1−i0000-11i−i−1+i31−i3−1+i31−i32ζ14−2ζ14000−ζ14+ζ20ζ14−ζ20ζ14+ζ20−ζ14−ζ2000001−i32−1+i32ζ14−ζ14−1−i31+i3−1−i31+i32ζ22−2ζ22000ζ4−ζ22−ζ4+ζ22ζ4+ζ22−ζ4−ζ2200001+i32−1−i32ζ22−ζ22
χ302-22-2−2i2i0001−i−1+i1+i−1−i0000-11−ii−1+i31−i3−1+i31−i3−2ζ142ζ14000−ζ14−ζ20ζ14+ζ20ζ14−ζ20−ζ14+ζ2000001−i32−1+i32−ζ14ζ14−1−i31+i3−1−i31+i3−2ζ222ζ22000−ζ4−ζ22ζ4+ζ22−ζ4+ζ22ζ4−ζ2200001+i32−1−i32−ζ22ζ22
χ312-22-2−2i2i000−1+i1−i−1−i1+i0000-11−ii−1+i31−i3−1+i31−i3−2ζ142ζ14000ζ14+ζ20−ζ14−ζ20−ζ14+ζ20ζ14−ζ2000001−i32−1+i32−ζ14ζ14−1−i31+i3−1−i31+i3−2ζ222ζ22000ζ4+ζ22−ζ4−ζ22ζ4−ζ22−ζ4+ζ2200001+i32−1−i32−ζ22ζ22
χ32333333-1-1-11111-1-1-1-10000−3+3i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i320000−3−3i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i320000
χ33333333-1-1-1-1-1-1-111110000−3+3i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i320000−3−3i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i320000
χ343333-3-311-1ii−i−i−i−iii0000−3+3i32−3+3i32−3+3i32−3+3i323−3i323−3i32−1+i32−1+i321−i32ζ14ζ14−ζ14−ζ14−ζ14−ζ14ζ14ζ140000−3−3i32−3−3i32−3−3i32−3−3i323+3i323+3i32−1−i32−1−i321+i32ζ22ζ22−ζ22−ζ22−ζ22−ζ22ζ22ζ220000
χ353333-3-311-1−i−iiiii−i−i0000−3+3i32−3+3i32−3+3i32−3+3i323−3i323−3i32−1+i32−1+i321−i32−ζ14−ζ14ζ14ζ14ζ14ζ14−ζ14−ζ140000−3−3i32−3−3i32−3−3i32−3−3i323+3i323+3i32−1−i32−1−i321+i32−ζ22−ζ22ζ22ζ22ζ22ζ22−ζ22−ζ220000
χ364-44-44i−4i000000000001-1−ii−2+2i32−2i3−2+2i32−2i34ζ14−4ζ1400000000000−1+i321−i32−ζ14ζ14−2−2i32+2i3−2−2i32+2i34ζ22−4ζ2200000000000−1−i321+i32−ζ22ζ22
χ374-44-4−4i4i000000000001-1i−i−2+2i32−2i3−2+2i32−2i3−4ζ144ζ1400000000000−1+i321−i32ζ14−ζ14−2−2i32+2i3−2−2i32+2i3−4ζ224ζ2200000000000−1−i321+i32ζ22−ζ22
χ386-6-22002-200000i2−i2i2−i20000−3+3i33−3i31−i3−1+i300−1+i31−i300000−ζ5−ζ23ζ5+ζ23−ζ5−ζ23ζ5+ζ230000−3−3i33+3i31+i3−1−i300−1−i31+i300000−ζ7−ζ13ζ7+ζ13−ζ7−ζ13ζ7+ζ130000
χ396-6-22002-200000−i2i2−i2i20000−3+3i33−3i31−i3−1+i300−1+i31−i300000ζ5+ζ23−ζ5−ζ23ζ5+ζ23−ζ5−ζ230000−3−3i33+3i31+i3−1−i300−1−i31+i300000ζ7+ζ13−ζ7−ζ13ζ7+ζ13−ζ7−ζ130000
χ406-6-2200-22000002−2−220000−3+3i33−3i31−i3−1+i3001−i3−1+i300000ζ5−ζ23−ζ5+ζ23−ζ5+ζ23ζ5−ζ230000−3−3i33+3i31+i3−1−i3001+i3−1−i300000−ζ7+ζ13ζ7−ζ13ζ7−ζ13−ζ7+ζ130000
χ416-6-2200-2200000−222−20000−3+3i33−3i31−i3−1+i3001−i3−1+i300000−ζ5+ζ23ζ5−ζ23ζ5−ζ23−ζ5+ζ230000−3−3i33+3i31+i3−1−i3001+i3−1−i300000ζ7−ζ13−ζ7+ζ13−ζ7+ζ13ζ7−ζ130000
χ421212-4-400000000000000000−6+6i3−6+6i32−2i32−2i300000000000000000−6−6i3−6−6i32+2i32+2i300000000000000000
χ43111111111111111111111−1−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+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ44111111111-1-1-1-1-1-1-1-11111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+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+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32
χ451111-1-1-1-11ii−i−iii−i−i11-1-1−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32ζ22ζ22−ζ22−ζ22ζ22ζ22−ζ22−ζ22−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32ζ14ζ14−ζ14−ζ14ζ14ζ14−ζ14−ζ14−1+i32−1+i321−i321−i32
χ461111-1-1-1-11−i−iii−i−iii11-1-1−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−ζ22−ζ22ζ22ζ22−ζ22−ζ22ζ22ζ22−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−ζ14−ζ14ζ14ζ14−ζ14−ζ14ζ14ζ14−1+i32−1+i321−i321−i32
χ4722222222200000000-1-1-1-1−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3000000001+i321+i321+i321+i32−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3000000001−i321−i321−i321−i32
χ482222-2-2-2-2200000000-1-111−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i3−1−i3000000001+i321+i32−1−i32−1−i32−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i3−1+i3000000001−i321−i32−1+i32−1+i32
χ492-22-22i−2i0001+i−1−i1−i−1+i0000-11i−i−1−i31+i3−1−i31+i32ζ22−2ζ22000−ζ4+ζ22ζ4−ζ22−ζ4−ζ22ζ4+ζ2200001+i32−1−i32ζ22−ζ22−1+i31−i3−1+i31−i32ζ14−2ζ14000ζ14−ζ20−ζ14+ζ20−ζ14−ζ20ζ14+ζ2000001−i32−1+i32ζ14−ζ14
χ502-22-22i−2i000−1−i1+i−1+i1−i0000-11i−i−1−i31+i3−1−i31+i32ζ22−2ζ22000ζ4−ζ22−ζ4+ζ22ζ4+ζ22−ζ4−ζ2200001+i32−1−i32ζ22−ζ22−1+i31−i3−1+i31−i32ζ14−2ζ14000−ζ14+ζ20ζ14−ζ20ζ14+ζ20−ζ14−ζ2000001−i32−1+i32ζ14−ζ14
χ512-22-2−2i2i0001−i−1+i1+i−1−i0000-11−ii−1−i31+i3−1−i31+i3−2ζ222ζ22000−ζ4−ζ22ζ4+ζ22−ζ4+ζ22ζ4−ζ2200001+i32−1−i32−ζ22ζ22−1+i31−i3−1+i31−i3−2ζ142ζ14000−ζ14−ζ20ζ14+ζ20ζ14−ζ20−ζ14+ζ2000001−i32−1+i32−ζ14ζ14
χ522-22-2−2i2i000−1+i1−i−1−i1+i0000-11−ii−1−i31+i3−1−i31+i3−2ζ222ζ22000ζ4+ζ22−ζ4−ζ22ζ4−ζ22−ζ4+ζ2200001+i32−1−i32−ζ22ζ22−1+i31−i3−1+i31−i3−2ζ142ζ14000ζ14+ζ20−ζ14−ζ20−ζ14+ζ20ζ14−ζ2000001−i32−1+i32−ζ14ζ14
χ53333333-1-1-11111-1-1-1-10000−3−3i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i320000−3+3i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i320000
χ54333333-1-1-1-1-1-1-111110000−3−3i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i320000−3+3i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i320000
χ553333-3-311-1ii−i−i−i−iii0000−3−3i32−3−3i32−3−3i32−3−3i323+3i323+3i32−1−i32−1−i321+i32ζ22ζ22−ζ22−ζ22−ζ22−ζ22ζ22ζ220000−3+3i32−3+3i32−3+3i32−3+3i323−3i323−3i32−1+i32−1+i321−i32ζ14ζ14−ζ14−ζ14−ζ14−ζ14ζ14ζ140000
χ563333-3-311-1−i−iiiii−i−i0000−3−3i32−3−3i32−3−3i32−3−3i323+3i323+3i32−1−i32−1−i321+i32−ζ22−ζ22ζ22ζ22ζ22ζ22−ζ22−ζ220000−3+3i32−3+3i32−3+3i32−3+3i323−3i323−3i32−1+i32−1+i321−i32−ζ14−ζ14ζ14ζ14ζ14ζ14−ζ14−ζ140000
χ574-44-44i−4i000000000001-1−ii−2−2i32+2i3−2−2i32+2i34ζ22−4ζ2200000000000−1−i321+i32−ζ22ζ22−2+2i32−2i3−2+2i32−2i34ζ14−4ζ1400000000000−1+i321−i32−ζ14ζ14
χ584-44-4−4i4i000000000001-1i−i−2−2i32+2i3−2−2i32+2i3−4ζ224ζ2200000000000−1−i321+i32ζ22−ζ22−2+2i32−2i3−2+2i32−2i3−4ζ144ζ1400000000000−1+i321−i32ζ14−ζ14
χ596-6-22002-200000i2−i2i2−i20000−3−3i33+3i31+i3−1−i300−1−i31+i300000−ζ7−ζ13ζ7+ζ13−ζ7−ζ13ζ7+ζ130000−3+3i33−3i31−i3−1+i300−1+i31−i300000−ζ5−ζ23ζ5+ζ23−ζ5−ζ23ζ5+ζ230000
χ606-6-22002-200000−i2i2−i2i20000−3−3i33+3i31+i3−1−i300−1−i31+i300000ζ7+ζ13−ζ7−ζ13ζ7+ζ13−ζ7−ζ130000−3+3i33−3i31−i3−1+i300−1+i31−i300000ζ5+ζ23−ζ5−ζ23ζ5+ζ23−ζ5−ζ230000
χ616-6-2200-22000002−2−220000−3−3i33+3i31+i3−1−i3001+i3−1−i300000−ζ7+ζ13ζ7−ζ13ζ7−ζ13−ζ7+ζ130000−3+3i33−3i31−i3−1+i3001−i3−1+i300000ζ5−ζ23−ζ5+ζ23−ζ5+ζ23ζ5−ζ230000
χ626-6-2200-2200000−222−20000−3−3i33+3i31+i3−1−i3001+i3−1−i300000ζ7−ζ13−ζ7+ζ13−ζ7+ζ13ζ7−ζ130000−3+3i33−3i31−i3−1+i3001−i3−1+i300000−ζ5+ζ23ζ5−ζ23ζ5−ζ23−ζ5+ζ230000
χ631212-4-400000000000000000−6−6i3−6−6i32+2i32+2i300000000000000000−6+6i3−6+6i32−2i32−2i300000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.