Finite Group Databasebeta

← Group #67913

Character table — Group #67913

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size111122444488888888888881111224444888888888888811112244448888888888888
order1222224444444448888888836666612121212121212121224242424242424243666661212121212121212122424242424242424
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1
χ311111111111-1-1-1-11111-1-1-1-111111111111-1-1-1-11111-1-1-1-111111111111-1-1-1-11111-1-1-1-1
χ411111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-11111
χ5111111-1-1-1-1111-1-1ii−i−iii−i−i111111-1-1-1-1111-1-1ii−i−iii−i−i111111-1-1-1-1111-1-1ii−i−iii−i−i
χ6111111-1-1-1-1111-1-1−i−iii−i−iii111111-1-1-1-1111-1-1−i−iii−i−iii111111-1-1-1-1111-1-1−i−iii−i−iii
χ7111111-1-1-1-11-1-111ii−i−i−i−iii111111-1-1-1-11-1-111ii−i−i−i−iii111111-1-1-1-11-1-111ii−i−i−i−iii
χ8111111-1-1-1-11-1-111−i−iiiii−i−i111111-1-1-1-11-1-111−i−iiiii−i−i111111-1-1-1-11-1-111−i−iiiii−i−i
χ92222222-2-22-20000000000002222222-2-22-20000000000002222222-2-22-2000000000000
χ10222222-222-2-2000000000000222222-222-2-2000000000000222222-222-2-2000000000000
χ1122-2-22-2200-2000002−22−2000022-2-22-2200-2000002−22−2000022-2-22-2200-2000002−22−20000
χ1222-2-22-2200-200000−22−22000022-2-22-2200-200000−22−22000022-2-22-2200-200000−22−220000
χ1322-2-22-2-200200000i2−i2−i2i2000022-2-22-2-200200000i2−i2−i2i2000022-2-22-2-200200000i2−i2−i2i20000
χ1422-2-22-2-200200000−i2i2i2−i2000022-2-22-2-200200000−i2i2i2−i2000022-2-22-2-200200000−i2i2i2−i20000
χ1522-2-2-2202i−2i00000000001−i−1+i1+i−1−i22-2-2-2202i−2i00000000001−i−1+i1+i−1−i22-2-2-2202i−2i00000000001−i−1+i1+i−1−i
χ1622-2-2-2202i−2i0000000000−1+i1−i−1−i1+i22-2-2-2202i−2i0000000000−1+i1−i−1−i1+i22-2-2-2202i−2i0000000000−1+i1−i−1−i1+i
χ1722-2-2-220−2i2i00000000001+i−1−i1−i−1+i22-2-2-220−2i2i00000000001+i−1−i1−i−1+i22-2-2-220−2i2i00000000001+i−1−i1−i−1+i
χ1822-2-2-220−2i2i0000000000−1−i1+i−1+i1−i22-2-2-220−2i2i0000000000−1−i1+i−1+i1−i22-2-2-220−2i2i0000000000−1−i1+i−1+i1−i
χ194444-4-4000000000000000004444-4-4000000000000000004444-4-400000000000000000
χ204-44-400000002i−2i00000000004-44-400000002i−2i00000000004-44-400000002i−2i0000000000
χ214-44-40000000−2i2i00000000004-44-40000000−2i2i00000000004-44-40000000−2i2i0000000000
χ224-4-440000000002i−2i000000004-4-440000000002i−2i000000004-4-440000000002i−2i00000000
χ234-4-44000000000−2i2i000000004-4-44000000000−2i2i000000004-4-44000000000−2i2i00000000
χ2411111111111111111111111−1+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−i32−1−i32−1−i32−1−i32−1−i32
χ25111111111111111-1-1-1-1-1-1-1-1−1+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−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−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32
χ2611111111111-1-1-1-11111-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+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+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32
χ2711111111111-1-1-1-1-1-1-1-11111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+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−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32
χ28111111-1-1-1-1111-1-1ii−i−iii−i−i−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i32ζ14ζ14−ζ14−ζ14ζ14ζ14−ζ14−ζ14−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i32ζ22ζ22−ζ22−ζ22ζ22ζ22−ζ22−ζ22
χ29111111-1-1-1-1111-1-1−i−iii−i−iii−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−ζ14−ζ14ζ14ζ14−ζ14−ζ14ζ14ζ14−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−ζ22−ζ22ζ22ζ22−ζ22−ζ22ζ22ζ22
χ30111111-1-1-1-11-1-111ii−i−i−i−iii−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i321−i32−1+i32−1+i32ζ14ζ14−ζ14−ζ14−ζ14−ζ14ζ14ζ14−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i321+i32−1−i32−1−i32ζ22ζ22−ζ22−ζ22−ζ22−ζ22ζ22ζ22
χ31111111-1-1-1-11-1-111−i−iiiii−i−i−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i321−i32−1+i32−1+i32−ζ14−ζ14ζ14ζ14ζ14ζ14−ζ14−ζ14−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i321+i32−1−i32−1−i32−ζ22−ζ22ζ22ζ22ζ22ζ22−ζ22−ζ22
χ322222222-2-22-2000000000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i31−i3000000000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i31+i3000000000000
χ33222222-222-2-2000000000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i3−1+i3−1+i31−i31−i3000000000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i3−1−i3−1−i31+i31+i3000000000000
χ3422-2-22-2200-2000002−22−20000−1+i3−1+i31−i31−i3−1+i31−i3−1+i3001−i300000ζ5−ζ23−ζ5+ζ23ζ5−ζ23−ζ5+ζ230000−1−i3−1−i31+i31+i3−1−i31+i3−1−i3001+i300000−ζ7+ζ13ζ7−ζ13−ζ7+ζ13ζ7−ζ130000
χ3522-2-22-2200-200000−22−220000−1+i3−1+i31−i31−i3−1+i31−i3−1+i3001−i300000−ζ5+ζ23ζ5−ζ23−ζ5+ζ23ζ5−ζ230000−1−i3−1−i31+i31+i3−1−i31+i3−1−i3001+i300000ζ7−ζ13−ζ7+ζ13ζ7−ζ13−ζ7+ζ130000
χ3622-2-22-2-200200000i2−i2−i2i20000−1+i3−1+i31−i31−i3−1+i31−i31−i300−1+i300000−ζ5−ζ23ζ5+ζ23ζ5+ζ23−ζ5−ζ230000−1−i3−1−i31+i31+i3−1−i31+i31+i300−1−i300000−ζ7−ζ13ζ7+ζ13ζ7+ζ13−ζ7−ζ130000
χ3722-2-22-2-200200000−i2i2i2−i20000−1+i3−1+i31−i31−i3−1+i31−i31−i300−1+i300000ζ5+ζ23−ζ5−ζ23−ζ5−ζ23ζ5+ζ230000−1−i3−1−i31+i31+i3−1−i31+i31+i300−1−i300000ζ7+ζ13−ζ7−ζ13−ζ7−ζ13ζ7+ζ130000
χ3822-2-2-2202i−2i00000000001−i−1+i1+i−1−i−1+i3−1+i31−i31−i31−i3−1+i302ζ14−2ζ140000000000−ζ14−ζ20ζ14+ζ20ζ14−ζ20−ζ14+ζ20−1−i3−1−i31+i31+i31+i3−1−i302ζ22−2ζ220000000000−ζ4−ζ22ζ4+ζ22−ζ4+ζ22ζ4−ζ22
χ3922-2-2-2202i−2i0000000000−1+i1−i−1−i1+i−1+i3−1+i31−i31−i31−i3−1+i302ζ14−2ζ140000000000ζ14+ζ20−ζ14−ζ20−ζ14+ζ20ζ14−ζ20−1−i3−1−i31+i31+i31+i3−1−i302ζ22−2ζ220000000000ζ4+ζ22−ζ4−ζ22ζ4−ζ22−ζ4+ζ22
χ4022-2-2-220−2i2i00000000001+i−1−i1−i−1+i−1+i3−1+i31−i31−i31−i3−1+i30−2ζ142ζ140000000000ζ14−ζ20−ζ14+ζ20−ζ14−ζ20ζ14+ζ20−1−i3−1−i31+i31+i31+i3−1−i30−2ζ222ζ220000000000−ζ4+ζ22ζ4−ζ22−ζ4−ζ22ζ4+ζ22
χ4122-2-2-220−2i2i0000000000−1−i1+i−1+i1−i−1+i3−1+i31−i31−i31−i3−1+i30−2ζ142ζ140000000000−ζ14+ζ20ζ14−ζ20ζ14+ζ20−ζ14−ζ20−1−i3−1−i31+i31+i31+i3−1−i30−2ζ222ζ220000000000ζ4−ζ22−ζ4+ζ22ζ4+ζ22−ζ4−ζ22
χ424444-4-400000000000000000−2+2i3−2+2i3−2+2i3−2+2i32−2i32−2i300000000000000000−2−2i3−2−2i3−2−2i3−2−2i32+2i32+2i300000000000000000
χ434-44-400000002i−2i0000000000−2+2i32−2i3−2+2i32−2i300000002ζ14−2ζ140000000000−2−2i32+2i3−2−2i32+2i300000002ζ22−2ζ220000000000
χ444-44-40000000−2i2i0000000000−2+2i32−2i3−2+2i32−2i30000000−2ζ142ζ140000000000−2−2i32+2i3−2−2i32+2i30000000−2ζ222ζ220000000000
χ454-4-440000000002i−2i00000000−2+2i32−2i32−2i3−2+2i30000000002ζ14−2ζ1400000000−2−2i32+2i32+2i3−2−2i30000000002ζ22−2ζ2200000000
χ464-4-44000000000−2i2i00000000−2+2i32−2i32−2i3−2+2i3000000000−2ζ142ζ1400000000−2−2i32+2i32+2i3−2−2i3000000000−2ζ222ζ2200000000
χ4711111111111111111111111−1−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+i32−1+i32−1+i32−1+i32−1+i32
χ48111111111111111-1-1-1-1-1-1-1-1−1−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+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+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i32
χ4911111111111-1-1-1-11111-1-1-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−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−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32
χ5011111111111-1-1-1-1-1-1-1-11111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−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+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32
χ51111111-1-1-1-1111-1-1ii−i−iii−i−i−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i32ζ22ζ22−ζ22−ζ22ζ22ζ22−ζ22−ζ22−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i32ζ14ζ14−ζ14−ζ14ζ14ζ14−ζ14−ζ14
χ52111111-1-1-1-1111-1-1−i−iii−i−iii−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−ζ22−ζ22ζ22ζ22−ζ22−ζ22ζ22ζ22−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−ζ14−ζ14ζ14ζ14−ζ14−ζ14ζ14ζ14
χ53111111-1-1-1-11-1-111ii−i−i−i−iii−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i321+i32−1−i32−1−i32ζ22ζ22−ζ22−ζ22−ζ22−ζ22ζ22ζ22−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i321−i32−1+i32−1+i32ζ14ζ14−ζ14−ζ14−ζ14−ζ14ζ14ζ14
χ54111111-1-1-1-11-1-111−i−iiiii−i−i−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i321+i32−1−i32−1−i32−ζ22−ζ22ζ22ζ22ζ22ζ22−ζ22−ζ22−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i321−i32−1+i32−1+i32−ζ14−ζ14ζ14ζ14ζ14ζ14−ζ14−ζ14
χ552222222-2-22-2000000000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i31+i3000000000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i31−i3000000000000
χ56222222-222-2-2000000000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i3−1−i3−1−i31+i31+i3000000000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i3−1+i3−1+i31−i31−i3000000000000
χ5722-2-22-2200-2000002−22−20000−1−i3−1−i31+i31+i3−1−i31+i3−1−i3001+i300000−ζ7+ζ13ζ7−ζ13−ζ7+ζ13ζ7−ζ130000−1+i3−1+i31−i31−i3−1+i31−i3−1+i3001−i300000ζ5−ζ23−ζ5+ζ23ζ5−ζ23−ζ5+ζ230000
χ5822-2-22-2200-200000−22−220000−1−i3−1−i31+i31+i3−1−i31+i3−1−i3001+i300000ζ7−ζ13−ζ7+ζ13ζ7−ζ13−ζ7+ζ130000−1+i3−1+i31−i31−i3−1+i31−i3−1+i3001−i300000−ζ5+ζ23ζ5−ζ23−ζ5+ζ23ζ5−ζ230000
χ5922-2-22-2-200200000i2−i2−i2i20000−1−i3−1−i31+i31+i3−1−i31+i31+i300−1−i300000−ζ7−ζ13ζ7+ζ13ζ7+ζ13−ζ7−ζ130000−1+i3−1+i31−i31−i3−1+i31−i31−i300−1+i300000−ζ5−ζ23ζ5+ζ23ζ5+ζ23−ζ5−ζ230000
χ6022-2-22-2-200200000−i2i2i2−i20000−1−i3−1−i31+i31+i3−1−i31+i31+i300−1−i300000ζ7+ζ13−ζ7−ζ13−ζ7−ζ13ζ7+ζ130000−1+i3−1+i31−i31−i3−1+i31−i31−i300−1+i300000ζ5+ζ23−ζ5−ζ23−ζ5−ζ23ζ5+ζ230000
χ6122-2-2-2202i−2i00000000001−i−1+i1+i−1−i−1−i3−1−i31+i31+i31+i3−1−i302ζ22−2ζ220000000000−ζ4−ζ22ζ4+ζ22−ζ4+ζ22ζ4−ζ22−1+i3−1+i31−i31−i31−i3−1+i302ζ14−2ζ140000000000−ζ14−ζ20ζ14+ζ20ζ14−ζ20−ζ14+ζ20
χ6222-2-2-2202i−2i0000000000−1+i1−i−1−i1+i−1−i3−1−i31+i31+i31+i3−1−i302ζ22−2ζ220000000000ζ4+ζ22−ζ4−ζ22ζ4−ζ22−ζ4+ζ22−1+i3−1+i31−i31−i31−i3−1+i302ζ14−2ζ140000000000ζ14+ζ20−ζ14−ζ20−ζ14+ζ20ζ14−ζ20
χ6322-2-2-220−2i2i00000000001+i−1−i1−i−1+i−1−i3−1−i31+i31+i31+i3−1−i30−2ζ222ζ220000000000−ζ4+ζ22ζ4−ζ22−ζ4−ζ22ζ4+ζ22−1+i3−1+i31−i31−i31−i3−1+i30−2ζ142ζ140000000000ζ14−ζ20−ζ14+ζ20−ζ14−ζ20ζ14+ζ20
χ6422-2-2-220−2i2i0000000000−1−i1+i−1+i1−i−1−i3−1−i31+i31+i31+i3−1−i30−2ζ222ζ220000000000ζ4−ζ22−ζ4+ζ22ζ4+ζ22−ζ4−ζ22−1+i3−1+i31−i31−i31−i3−1+i30−2ζ142ζ140000000000−ζ14+ζ20ζ14−ζ20ζ14+ζ20−ζ14−ζ20
χ654444-4-400000000000000000−2−2i3−2−2i3−2−2i3−2−2i32+2i32+2i300000000000000000−2+2i3−2+2i3−2+2i3−2+2i32−2i32−2i300000000000000000
χ664-44-400000002i−2i0000000000−2−2i32+2i3−2−2i32+2i300000002ζ22−2ζ220000000000−2+2i32−2i3−2+2i32−2i300000002ζ14−2ζ140000000000
χ674-44-40000000−2i2i0000000000−2−2i32+2i3−2−2i32+2i30000000−2ζ222ζ220000000000−2+2i32−2i3−2+2i32−2i30000000−2ζ142ζ140000000000
χ684-4-440000000002i−2i00000000−2−2i32+2i32+2i3−2−2i30000000002ζ22−2ζ2200000000−2+2i32−2i32−2i3−2+2i30000000002ζ14−2ζ1400000000
χ694-4-44000000000−2i2i00000000−2−2i32+2i32+2i3−2−2i3000000000−2ζ222ζ2200000000−2+2i32−2i32−2i3−2+2i3000000000−2ζ142ζ1400000000

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