Finite Group Databasebeta

← Group #13052102

Character table — Group #13052102

Order 1344.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1122244667777881212121414141414141414141414142424242424242828282828282828282828282856565656565656565656
order122442471433664814282866881212121224242424142828285656668881212242424242424481212121224242424
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111-1-11111-1-1-1-111111111-1-1-111-1-1-1-1-1-1-1-111-1-111-1-1
χ31111111111111-1-111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111-1-111111-1-11111-1-1-1-111-1-1-1-111-1-1-111-1-1-1-1-1-111-1-111-1-111
χ5111111111−1−i32−1+i32−1−i32−1+i3211111−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32111111−1−i32−1+i32111−1−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
χ6111111111−1−i32−1+i32−1−i32−1+i3211111−1−i32−1+i32-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32111111−1−i32−1+i32-1-1-1−1−i32−1+i321+i321+i321+i321−i321−i321−i32-1-1−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i32
χ7111111111−1−i32−1+i32−1−i32−1+i32-1-1111−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i3211-1-1-1-1−1−i32−1+i32111−1−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
χ8111111111−1−i32−1+i32−1−i32−1+i32-1-1111−1−i32−1+i32-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i3211-1-1-1-1−1−i32−1+i32-1-1-1−1−i32−1+i321+i321+i321+i321−i321−i321−i32111+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32
χ9111111111−1+i32−1−i32−1+i32−1−i3211111−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32111111−1+i32−1−i32111−1+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
χ10111111111−1+i32−1−i32−1+i32−1−i3211111−1+i32−1−i32-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32111111−1+i32−1−i32-1-1-1−1+i32−1−i321−i321−i321−i321+i321+i321+i32-1-1−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i32
χ11111111111−1+i32−1−i32−1+i32−1−i32-1-1111−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i3211-1-1-1-1−1+i32−1−i32111−1+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
χ12111111111−1+i32−1−i32−1+i32−1−i32-1-1111−1+i32−1−i32-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i3211-1-1-1-1−1+i32−1−i32-1-1-1−1+i32−1−i321−i321−i321−i321+i321+i321+i32111−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i32
χ1311111-1-11111111-1111111111111111-1-111-1-1-1-11-1-1-1-11-1-11-1-11-11111-1-1-1-1
χ1411111-1-11111111-111111-1-11111-1-1-1-1-1-111-1-1-1-1-111-1-1-111-111-1111-1-1-1-111
χ1511111-1-1111111-11111111111111111-1-1-1-111-1-11-1-1-1-11-1-11-1-1-11-1-1-1-11111
χ1611111-1-1111111-1111111-1-11111-1-1-1-1-1-1-1-111-1-1-111-1-1-111-1111-1-1-11111-1-1
χ1711111-1-111−1−i32−1+i32−1−i32−1+i321-1111−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-111-1-11+i321−i321-1-11+i321−i32−1−i321+i321+i32−1+i321−i321−i321-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32
χ1811111-1-111−1−i32−1+i32−1−i32−1+i321-1111−1−i32−1+i32-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-1-111-1-11+i321−i32-1111+i321−i321+i32−1−i32−1−i321−i32−1+i32−1+i32-11−1−i32−1+i321+i321−i321+i321−i32−1−i32−1+i32
χ1911111-1-111−1−i32−1+i32−1−i32−1+i32-11111−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-1111+i321−i321-1-11+i321−i32−1−i321+i321+i32−1+i321−i321−i32-111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32
χ2011111-1-111−1−i32−1+i32−1−i32−1+i32-11111−1−i32−1+i32-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-1-1-1-1111+i321−i32-1111+i321−i321+i32−1−i32−1−i321−i32−1+i32−1+i321-11+i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i32
χ2111111-1-111−1+i32−1−i32−1+i32−1−i321-1111−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-111-1-11−i321+i321-1-11−i321+i32−1+i321−i321−i32−1−i321+i321+i321-1−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32
χ2211111-1-111−1+i32−1−i32−1+i32−1−i321-1111−1+i32−1−i32-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32-1-111-1-11−i321+i32-1111−i321+i321−i32−1+i32−1+i321+i32−1−i32−1−i32-11−1+i32−1−i321−i321+i321−i321+i32−1+i32−1−i32
χ2311111-1-111−1+i32−1−i32−1+i32−1−i32-11111−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-1111−i321+i321-1-11−i321+i32−1+i321−i321−i32−1−i321+i321+i32-111−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i32
χ2411111-1-111−1+i32−1−i32−1+i32−1−i32-11111−1+i32−1−i32-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32-1-1-1-1111−i321+i32-1111−i321+i321−i32−1+i32−1+i321+i32−1−i32−1−i321-11−i321+i32−1+i32−1−i32−1+i32−1−i321−i321+i32
χ25222-2-200222222002-2-22200-2-2-2-200000000000002i−2i0002i−2i02i−2i0000000000
χ26222-2-200222222002-2-22200-2-2-2-20000000000000−2i2i000−2i2i0−2i2i0000000000
χ27222-2-20022−1−i3−1+i3−1−i3−1+i3002-2-2−1−i3−1+i3001+i31+i31−i31−i300000000000002i−2i0002ζ22+2ζ46+2ζ94+2ζ118+2ζ142+2ζ166−2ζ22−2ζ46−2ζ94−2ζ118−2ζ142−2ζ16602ζ38+2ζ62+2ζ86+2ζ110+2ζ134+2ζ158−2ζ38−2ζ62−2ζ86−2ζ110−2ζ134−2ζ1580000000000
χ28222-2-20022−1−i3−1+i3−1−i3−1+i3002-2-2−1−i3−1+i3001+i31+i31−i31−i30000000000000−2i2i000−2ζ22−2ζ46−2ζ94−2ζ118−2ζ142−2ζ1662ζ22+2ζ46+2ζ94+2ζ118+2ζ142+2ζ1660−2ζ38−2ζ62−2ζ86−2ζ110−2ζ134−2ζ1582ζ38+2ζ62+2ζ86+2ζ110+2ζ134+2ζ1580000000000
χ29222-2-20022−1+i3−1−i3−1+i3−1−i3002-2-2−1+i3−1−i3001−i31−i31+i31+i300000000000002i−2i0002ζ38+2ζ62+2ζ86+2ζ110+2ζ134+2ζ158−2ζ38−2ζ62−2ζ86−2ζ110−2ζ134−2ζ15802ζ22+2ζ46+2ζ94+2ζ118+2ζ142+2ζ166−2ζ22−2ζ46−2ζ94−2ζ118−2ζ142−2ζ1660000000000
χ30222-2-20022−1+i3−1−i3−1+i3−1−i3002-2-2−1+i3−1−i3001−i31−i31+i31+i30000000000000−2i2i000−2ζ38−2ζ62−2ζ86−2ζ110−2ζ134−2ζ1582ζ38+2ζ62+2ζ86+2ζ110+2ζ134+2ζ1580−2ζ22−2ζ46−2ζ94−2ζ118−2ζ142−2ζ1662ζ22+2ζ46+2ζ94+2ζ118+2ζ142+2ζ1660000000000
χ3122-22-22-222222200-2-22-2-2002-22-200002-2000022000-2-20000000000000000
χ3222-22-22-222−1−i3−1+i3−1−i3−1+i300-2-221+i31−i300−1−i31+i3−1+i31−i300002-20000−1−i3−1+i30001+i31−i30000000000000000
χ3322-22-22-222−1+i3−1−i3−1+i3−1−i300-2-221−i31+i300−1+i31−i3−1−i31+i300002-20000−1+i3−1−i30001−i31+i30000000000000000
χ3422-22-2-2222222200-2-22-2-2002-22-20000-220000-2-2000220000000000000000
χ3522-22-2-2222−1−i3−1+i3−1−i3−1+i300-2-221+i31−i300−1−i31+i3−1+i31−i30000-2200001+i31−i3000−1−i3−1+i30000000000000000
χ3622-22-2-2222−1+i3−1−i3−1+i3−1−i300-2-221−i31+i300−1+i31−i3−1−i31+i30000-2200001−i31+i3000−1+i3−1−i30000000000000000
χ3722-2-220022222200-22-2-2-222-22-22222200000000-20000-200-2000000000000
χ3822-2-220022222200-22-2-2-2-2-2-22-22-2-2-2-200000000200002002000000000000
χ3922-2-220022−1−i3−1+i3−1−i3−1+i300-22-21+i31−i3221+i3−1−i31−i3−1+i3−1−i3−1−i3−1+i3−1+i300000000-200001+i3001−i3000000000000
χ4022-2-220022−1−i3−1+i3−1−i3−1+i300-22-21+i31−i3-2-21+i3−1−i31−i3−1+i31+i31+i31−i31−i30000000020000−1−i300−1+i3000000000000
χ4122-2-220022−1+i3−1−i3−1+i3−1−i300-22-21−i31+i3221−i3−1+i31+i3−1−i3−1+i3−1+i3−1−i3−1−i300000000-200001−i3001+i3000000000000
χ4222-2-220022−1+i3−1−i3−1+i3−1−i300-22-21−i31+i3-2-21−i3−1+i31+i3−1−i31−i31−i31+i31+i30000000020000−1+i300−1−i3000000000000
χ434-4000004-444-4-4000000022−22000022−2222−2200000000000000000000000000000
χ444-4000004-444-4-40000000−22220000−2222−222200000000000000000000000000000
χ454-4000004-4−2−2i3−2+2i32+2i32−2i3000000022−220000−2ζ13+2ζ31−2ζ37+2ζ55−2ζ61+2ζ79−2ζ85+2ζ103−2ζ109+2ζ127+2ζ151−2ζ1572ζ13−2ζ31+2ζ37−2ζ55+2ζ61−2ζ79+2ζ85−2ζ103+2ζ109−2ζ127−2ζ151+2ζ157−2ζ5+2ζ23−2ζ29+2ζ47−2ζ53+2ζ71+2ζ95−2ζ101−2ζ125+2ζ143−2ζ149+2ζ1672ζ5−2ζ23+2ζ29−2ζ47+2ζ53−2ζ71−2ζ95+2ζ101+2ζ125−2ζ143+2ζ149−2ζ16700000000000000000000000000000
χ464-4000004-4−2−2i3−2+2i32+2i32−2i30000000−222200002ζ13−2ζ31+2ζ37−2ζ55+2ζ61−2ζ79+2ζ85−2ζ103+2ζ109−2ζ127−2ζ151+2ζ157−2ζ13+2ζ31−2ζ37+2ζ55−2ζ61+2ζ79−2ζ85+2ζ103−2ζ109+2ζ127+2ζ151−2ζ1572ζ5−2ζ23+2ζ29−2ζ47+2ζ53−2ζ71−2ζ95+2ζ101+2ζ125−2ζ143+2ζ149−2ζ167−2ζ5+2ζ23−2ζ29+2ζ47−2ζ53+2ζ71+2ζ95−2ζ101−2ζ125+2ζ143−2ζ149+2ζ16700000000000000000000000000000
χ474-4000004-4−2+2i3−2−2i32−2i32+2i3000000022−220000−2ζ5+2ζ23−2ζ29+2ζ47−2ζ53+2ζ71+2ζ95−2ζ101−2ζ125+2ζ143−2ζ149+2ζ1672ζ5−2ζ23+2ζ29−2ζ47+2ζ53−2ζ71−2ζ95+2ζ101+2ζ125−2ζ143+2ζ149−2ζ167−2ζ13+2ζ31−2ζ37+2ζ55−2ζ61+2ζ79−2ζ85+2ζ103−2ζ109+2ζ127+2ζ151−2ζ1572ζ13−2ζ31+2ζ37−2ζ55+2ζ61−2ζ79+2ζ85−2ζ103+2ζ109−2ζ127−2ζ151+2ζ15700000000000000000000000000000
χ484-4000004-4−2+2i3−2−2i32−2i32+2i30000000−222200002ζ5−2ζ23+2ζ29−2ζ47+2ζ53−2ζ71−2ζ95+2ζ101+2ζ125−2ζ143+2ζ149−2ζ167−2ζ5+2ζ23−2ζ29+2ζ47−2ζ53+2ζ71+2ζ95−2ζ101−2ζ125+2ζ143−2ζ149+2ζ1672ζ13−2ζ31+2ζ37−2ζ55+2ζ61−2ζ79+2ζ85−2ζ103+2ζ109−2ζ127−2ζ151+2ζ157−2ζ13+2ζ31−2ζ37+2ζ55−2ζ61+2ζ79−2ζ85+2ζ103−2ζ109+2ζ127+2ζ151−2ζ15700000000000000000000000000000
χ496666666-1-1000066-1-1-1000000000000-1-1-1-1-1-100000000000000000000000
χ506666666-1-10000-6-6-1-1-1000000000000-1-1111100000000000000000000000
χ5166666-6-6-1-100006-6-1-1-100000000000011-1-11100000000000000000000000
χ5266666-6-6-1-10000-66-1-1-10000000000001111-1-100000000000000000000000
χ5366-66-66-6-1-100000011-1000000000000-11−i7i7−i7i700000000000000000000000
χ5466-66-66-6-1-100000011-1000000000000-11i7−i7i7−i700000000000000000000000
χ5566-66-6-66-1-100000011-10000000000001-1−i7i7i7−i700000000000000000000000
χ5666-66-6-66-1-100000011-10000000000001-1i7−i7−i7i700000000000000000000000
χ57121212-12-1200-2-2000000-22200000000000000000000000000000000000000000
χ581212-12-121200-2-20000002-2200000000000000000000000000000000000000000
χ5924-2400000-4400000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 168 (ζ168 = 1); i = ζ42.