Finite Group Databasebeta

← Group #67974

Character table — Group #67974

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51
size112444444488161616161611244444448816161616161124444444881616161616
order12244488882444488366121212242424246121212122424366121212242424246121212122424
χ1111111111111111111111111111111111111111111111111111
χ21111111111111-1-1-1-11111111111111-1-1-1-11111111111111-1-1-1-1
χ31111111111-1-1-1i−ii−i1111111111-1-1-1i−ii−i1111111111-1-1-1i−ii−i
χ41111111111-1-1-1−ii−ii1111111111-1-1-1−ii−ii1111111111-1-1-1−ii−ii
χ5111111-1-1-1-111-111-1-1111111-1-1-1-111-111-1-1111111-1-1-1-111-111-1-1
χ6111111-1-1-1-111-1-1-111111111-1-1-1-111-1-1-111111111-1-1-1-111-1-1-111
χ7111111-1-1-1-1-1-11i−i−ii111111-1-1-1-1-1-11i−i−ii111111-1-1-1-1-1-11i−i−ii
χ8111111-1-1-1-1-1-11−iii−i111111-1-1-1-1-1-11−iii−i111111-1-1-1-1-1-11−iii−i
χ9222-2-2200002-200000222-2-2200002-200000222-2-2200002-200000
χ10222-2-220000-2200000222-2-220000-2200000222-2-220000-2200000
χ1144400-40000000000044400-40000000000044400-400000000000
χ1244-40002i2i−2i−2i000000044-40002i2i−2i−2i000000044-40002i2i−2i−2i0000000
χ1344-4000−2i−2i2i2i000000044-4000−2i−2i2i2i000000044-4000−2i−2i2i2i0000000
χ144-402i−2i02ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ1300000004-402i−2i02ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ1300000004-402i−2i02ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ130000000
χ154-402i−2i0−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ1300000004-402i−2i0−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ1300000004-402i−2i0−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ130000000
χ164-40−2i2i02ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ2300000004-40−2i2i02ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ2300000004-40−2i2i02ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ230000000
χ174-40−2i2i0−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ2300000004-40−2i2i0−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ2300000004-40−2i2i0−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ230000000
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
χ191111111111111-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+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+i32
χ201111111111-1-1-1i−ii−i−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32ζ14−ζ14ζ14−ζ14−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32ζ22−ζ22ζ22−ζ22
χ211111111111-1-1-1−ii−ii−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−ζ14ζ14−ζ14ζ14−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−ζ22ζ22−ζ22ζ22
χ22111111-1-1-1-111-111-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i32
χ23111111-1-1-1-111-1-1-111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32
χ24111111-1-1-1-1-1-11i−i−ii−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32ζ14−ζ14−ζ14ζ14−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32ζ22−ζ22−ζ22ζ22
χ25111111-1-1-1-1-1-11−iii−i−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−ζ14ζ14ζ14−ζ14−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−ζ22ζ22ζ22−ζ22
χ26222-2-2200002-200000−1+i3−1+i3−1+i31−i31−i3−1+i30000−1+i31−i300000−1−i3−1−i3−1−i31+i31+i3−1−i30000−1−i31+i300000
χ27222-2-220000-2200000−1+i3−1+i3−1+i31−i31−i3−1+i300001−i3−1+i300000−1−i3−1−i3−1−i31+i31+i3−1−i300001+i3−1−i300000
χ2844400-400000000000−2+2i3−2+2i3−2+2i3002−2i300000000000−2−2i3−2−2i3−2−2i3002+2i300000000000
χ2944-40002i2i−2i−2i0000000−2+2i3−2+2i32−2i30002ζ142ζ14−2ζ14−2ζ140000000−2−2i3−2−2i32+2i30002ζ222ζ22−2ζ22−2ζ220000000
χ3044-4000−2i−2i2i2i0000000−2+2i3−2+2i32−2i3000−2ζ14−2ζ142ζ142ζ140000000−2−2i3−2−2i32+2i3000−2ζ22−2ζ222ζ222ζ220000000
χ314-402i−2i02ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ130000000−2+2i32−2i302ζ14−2ζ140−2ζ232ζ23−2ζ52ζ50000000−2−2i32+2i302ζ22−2ζ220−2ζ72ζ7−2ζ132ζ130000000
χ324-402i−2i0−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ130000000−2+2i32−2i302ζ14−2ζ1402ζ23−2ζ232ζ5−2ζ50000000−2−2i32+2i302ζ22−2ζ2202ζ7−2ζ72ζ13−2ζ130000000
χ334-40−2i2i02ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ230000000−2+2i32−2i30−2ζ142ζ140−2ζ52ζ5−2ζ232ζ230000000−2−2i32+2i30−2ζ222ζ220−2ζ132ζ13−2ζ72ζ70000000
χ344-40−2i2i0−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ230000000−2+2i32−2i30−2ζ142ζ1402ζ5−2ζ52ζ23−2ζ230000000−2−2i32+2i30−2ζ222ζ2202ζ13−2ζ132ζ7−2ζ70000000
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
χ361111111111111-1-1-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−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−i32
χ371111111111-1-1-1i−ii−i−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32ζ22−ζ22ζ22−ζ22−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32ζ14−ζ14ζ14−ζ14
χ381111111111-1-1-1−ii−ii−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−ζ22ζ22−ζ22ζ22−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−ζ14ζ14−ζ14ζ14
χ39111111-1-1-1-111-111-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i32
χ40111111-1-1-1-111-1-1-111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32
χ41111111-1-1-1-1-1-11i−i−ii−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32ζ22−ζ22−ζ22ζ22−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32ζ14−ζ14−ζ14ζ14
χ42111111-1-1-1-1-1-11−iii−i−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−ζ22ζ22ζ22−ζ22−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−ζ14ζ14ζ14−ζ14
χ43222-2-2200002-200000−1−i3−1−i3−1−i31+i31+i3−1−i30000−1−i31+i300000−1+i3−1+i3−1+i31−i31−i3−1+i30000−1+i31−i300000
χ44222-2-220000-2200000−1−i3−1−i3−1−i31+i31+i3−1−i300001+i3−1−i300000−1+i3−1+i3−1+i31−i31−i3−1+i300001−i3−1+i300000
χ4544400-400000000000−2−2i3−2−2i3−2−2i3002+2i300000000000−2+2i3−2+2i3−2+2i3002−2i300000000000
χ4644-40002i2i−2i−2i0000000−2−2i3−2−2i32+2i30002ζ222ζ22−2ζ22−2ζ220000000−2+2i3−2+2i32−2i30002ζ142ζ14−2ζ14−2ζ140000000
χ4744-4000−2i−2i2i2i0000000−2−2i3−2−2i32+2i3000−2ζ22−2ζ222ζ222ζ220000000−2+2i3−2+2i32−2i3000−2ζ14−2ζ142ζ142ζ140000000
χ484-402i−2i02ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ130000000−2−2i32+2i302ζ22−2ζ220−2ζ72ζ7−2ζ132ζ130000000−2+2i32−2i302ζ14−2ζ140−2ζ232ζ23−2ζ52ζ50000000
χ494-402i−2i0−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ130000000−2−2i32+2i302ζ22−2ζ2202ζ7−2ζ72ζ13−2ζ130000000−2+2i32−2i302ζ14−2ζ1402ζ23−2ζ232ζ5−2ζ50000000
χ504-40−2i2i02ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ230000000−2−2i32+2i30−2ζ222ζ220−2ζ132ζ13−2ζ72ζ70000000−2+2i32−2i30−2ζ142ζ140−2ζ52ζ5−2ζ232ζ230000000
χ514-40−2i2i0−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ230000000−2−2i32+2i30−2ζ222ζ2202ζ13−2ζ132ζ7−2ζ70000000−2+2i32−2i30−2ζ142ζ1402ζ5−2ζ52ζ23−2ζ230000000

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