Finite Group Databasebeta

← Group #72245629

Character table — Group #72245629

Order 2016.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11222446666777781212121212121414141414141818242424282828282828282828282828282828283636364242424256565656568484848484848484
order123462122471433666214142128423366121214144242842666681212242424242424242414142866121266666466812122424
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-111-1-1-111-1-1-1-1-1-1-1-11111111-111-1-1-111-1-1-1-1-1
χ311111111111−1−i32−1+i32−1−i32−1+i321111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32
χ411111111111−1−i32−1+i32−1−i32−1+i321111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211111-1−1−i32−1+i321+i321−i32-1−1−i32−1+i32-1-11+i321−i321+i321+i321−i321−i32111−1−i32−1+i32−1−i32−1+i32-1−1−i32−1+i321+i321−i32-1−1−i32−1+i32-11+i321−i321+i321−i32
χ511111111111−1+i32−1−i32−1+i32−1−i321111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32
χ611111111111−1+i32−1−i32−1+i32−1−i321111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211111-1−1+i32−1−i321−i321+i32-1−1+i32−1−i32-1-11−i321+i321−i321−i321+i321+i32111−1+i32−1−i32−1+i32−1−i32-1−1+i32−1−i321−i321+i32-1−1+i32−1−i32-11−i321+i321−i321+i32
χ71111111-1-11111111-111111111111-1-11111111111111111111-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1
χ81111111-1-11111111-111111111111-1-1111-111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-111111
χ91111111-1-111−1−i32−1+i32−1−i32−1+i321-111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-11111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-11+i321−i321+i321−i321−1−i32−1+i32−1−i32−1+i32-11+i321−i32-11+i321−i321+i321−i32
χ101111111-1-111−1−i32−1+i32−1−i32−1+i321-111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1111-1−1−i32−1+i321+i321−i32-1−1−i32−1+i32-1-11+i321−i321+i321+i321−i321−i32-1-1-11+i321−i321+i321−i32-1−1−i32−1+i321+i321−i3211+i321−i321−1−i32−1+i32−1−i32−1+i32
χ111111111-1-111−1+i32−1−i32−1+i32−1−i321-111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-11111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-11−i321+i321−i321+i321−1+i32−1−i32−1+i32−1−i32-11−i321+i32-11−i321+i321−i321+i32
χ121111111-1-111−1+i32−1−i32−1+i32−1−i321-111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1111-1−1+i32−1−i321−i321+i32-1−1+i32−1−i32-1-11−i321+i321−i321−i321+i321+i32-1-1-11−i321+i321−i321+i32-1−1+i32−1−i321−i321+i3211−i321+i321−1+i32−1−i32−1+i32−1−i32
χ1311111-1111111111-1-1-1-111111111111-1-111-1-111-111-1-1-1-1-1-1-1-1-1-1111111-1-1111-1-1-111-1-1
χ1411111-1111111111-1-1-1-111111111111-1-11-1-1-1-1-111111111111-1-111111-1-1-1-1-1-1-1-11-1-111
χ1511111-111111−1−i32−1+i32−1−i32−1+i32-1-1-1-1111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211-1-1111+i321−i32−1−i32−1+i32-1−1−i32−1+i32-1-11+i321−i321+i321+i321−i321−i32-1-11−1−i32−1+i32−1−i32−1+i3211+i321−i32−1−i32−1+i3211+i321−i32-1−1−i32−1+i321+i321−i32
χ1611111-111111−1−i32−1+i32−1−i32−1+i32-1-1-1-1111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211-1-11-11+i321−i321+i321−i321−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-11−1−i32−1+i32−1−i32−1+i32-11+i321−i321+i321−i32-11+i321−i3211+i321−i32−1−i32−1+i32
χ1711111-111111−1+i32−1−i32−1+i32−1−i32-1-1-1-1111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211-1-1111−i321+i32−1+i32−1−i32-1−1+i32−1−i32-1-11−i321+i321−i321−i321+i321+i32-1-11−1+i32−1−i32−1+i32−1−i3211−i321+i32−1+i32−1−i3211−i321+i32-1−1+i32−1−i321−i321+i32
χ1811111-111111−1+i32−1−i32−1+i32−1−i32-1-1-1-1111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211-1-11-11−i321+i321−i321+i321−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-11−1+i32−1−i32−1+i32−1−i32-11−i321+i321−i321+i32-11−i321+i3211−i321+i32−1+i32−1−i32
χ1911111-11-1-1111111-11-1-1111111111-1-1-1-111-1-111-111-1-1-1-1-1-1-1-111-1-1-1-1-11-1-111-1111-1-111
χ2011111-11-1-1111111-11-1-1111111111-1-1-1-11-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1111-111-1-1
χ2111111-11-1-111−1−i32−1+i32−1−i32−1+i32-11-1-1111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1-1-1111+i321−i32−1−i32−1+i32-1−1−i32−1+i32-1-11+i321−i321+i321+i321−i321−i3211-11+i321−i321+i321−i3211+i321−i32−1−i32−1+i32-1−1−i32−1+i3211+i321−i32−1−i32−1+i32
χ2211111-11-1-111−1−i32−1+i32−1−i32−1+i32-11-1-1111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1-1-11-11+i321−i321+i321−i321−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211-11+i321−i321+i321−i32-11+i321−i321+i321−i321−1−i32−1+i32-1−1−i32−1+i321+i321−i32
χ2311111-11-1-111−1+i32−1−i32−1+i32−1−i32-11-1-1111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1-1-1111−i321+i32−1+i32−1−i32-1−1+i32−1−i32-1-11−i321+i321−i321−i321+i321+i3211-11−i321+i321−i321+i3211−i321+i32−1+i32−1−i32-1−1+i32−1−i3211−i321+i32−1+i32−1−i32
χ2411111-11-1-111−1+i32−1−i32−1+i32−1−i32-11-1-1111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1-1-11-11−i321+i321−i321+i321−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211-11−i321+i321−i321+i32-11−i321+i321−i321+i321−1+i32−1−i32-1−1+i32−1−i321−i321+i32
χ25222-220-22-222222200002-222222-2-22200-2000000-2-20000000000-222-2-20000000000000
χ26222-220-22-222−1−i3−1+i3−1−i3−1+i300002-22−1−i3−1+i3−1−i3−1+i31+i31−i32200-20000001+i31−i30000000000-2−1−i3−1+i31+i31−i30000000000000
χ27222-220-22-222−1+i3−1−i3−1+i3−1−i300002-22−1+i3−1−i3−1+i3−1−i31−i31+i32200-20000001−i31+i30000000000-2−1+i3−1−i31−i31+i30000000000000
χ28222-220-2-2222222200002-222222-2-2-2-200-2000000-2-200000000002-2-2220000000000000
χ29222-220-2-2222−1−i3−1+i3−1−i3−1+i300002-22−1−i3−1+i3−1−i3−1+i31+i31−i3-2-200-20000001+i31−i3000000000021+i31−i3−1−i3−1+i30000000000000
χ30222-220-2-2222−1+i3−1−i3−1+i3−1−i300002-22−1+i3−1−i3−1+i3−1−i31−i31+i3-2-200-20000001−i31+i3000000000021−i31+i3−1+i3−1−i30000000000000
χ3122-12-12-100222222-1022-12-1-1-1-1-12200-1-1-1222222-1-1-1-122-1-1-1-10000000-1-1-1-1-100000000
χ3222-12-12-100222222-1022-12-1-1-1-1-12200-1-1-1-222-2-2-2-1-111-2-2111100000001-1-11100000000
χ3322-12-12-10022−1−i3−1+i3−1−i3−1+i3-1022-12-11+i321−i321+i321−i32−1−i3−1+i300-1-1-12−1−i3−1+i3−1−i3−1+i321+i321−i32-1-1−1−i3−1+i31+i321+i321−i321−i320000000-11+i321−i321+i321−i3200000000
χ3422-12-12-10022−1−i3−1+i3−1−i3−1+i3-1022-12-11+i321−i321+i321−i32−1−i3−1+i300-1-1-1-2−1−i3−1+i31+i31−i3-21+i321−i32111+i31−i3−1−i32−1−i32−1+i32−1+i32000000011+i321−i32−1−i32−1+i3200000000
χ3522-12-12-10022−1+i3−1−i3−1+i3−1−i3-1022-12-11−i321+i321−i321+i32−1+i3−1−i300-1-1-12−1+i3−1−i3−1+i3−1−i321−i321+i32-1-1−1+i3−1−i31−i321−i321+i321+i320000000-11−i321+i321−i321+i3200000000
χ3622-12-12-10022−1+i3−1−i3−1+i3−1−i3-1022-12-11−i321+i321−i321+i32−1+i3−1−i300-1-1-1-2−1+i3−1−i31−i31+i3-21−i321+i32111−i31+i3−1+i32−1+i32−1−i32−1−i32000000011−i321+i32−1+i32−1−i3200000000
χ3722-12-1-2-10022222210-2-2-12-1-1-1-1-1220011-12-2-222-2-1-111-2-211110000000-111-1-100000000
χ3822-12-1-2-10022222210-2-2-12-1-1-1-1-1220011-1-2-2-2-2-22-1-1-1-122-1-1-1-100000001111100000000
χ3922-12-1-2-10022−1−i3−1+i3−1−i3−1+i310-2-2-12-11+i321−i321+i321−i32−1−i3−1+i30011-121+i31−i3−1−i3−1+i3-21+i321−i32111+i31−i3−1−i32−1−i32−1+i32−1+i320000000-1−1−i32−1+i321+i321−i3200000000
χ4022-12-1-2-10022−1−i3−1+i3−1−i3−1+i310-2-2-12-11+i321−i321+i321−i32−1−i3−1+i30011-1-21+i31−i31+i31−i321+i321−i32-1-1−1−i3−1+i31+i321+i321−i321−i3200000001−1−i32−1+i32−1−i32−1+i3200000000
χ4122-12-1-2-10022−1+i3−1−i3−1+i3−1−i310-2-2-12-11−i321+i321−i321+i32−1+i3−1−i30011-121−i31+i3−1+i3−1−i3-21−i321+i32111−i31+i3−1+i32−1+i32−1−i32−1−i320000000-1−1+i32−1−i321−i321+i3200000000
χ4222-12-1-2-10022−1+i3−1−i3−1+i3−1−i310-2-2-12-11−i321+i321−i321+i32−1+i3−1−i30011-1-21−i31+i31−i31+i321−i321+i32-1-1−1+i3−1−i31−i321−i321+i321+i3200000001−1+i32−1−i32−1+i32−1−i3200000000
χ4344-2-4-202004444440000-2-4-2-2-2-2-2-4-400002000000220000000000000000000000000000
χ4444-2-4-2020044−2−2i3−2+2i3−2−2i3−2+2i30000-2-4-21+i31−i31+i31−i32+2i32−2i300002000000−1−i3−1+i30000000000000000000000000000
χ4544-2-4-2020044−2+2i3−2−2i3−2+2i3−2−2i30000-2-4-21−i31+i31−i31+i32−2i32+2i300002000000−1+i3−1−i30000000000000000000000000000
χ464-440-400004-444-4-4000040-444-4-40000000000000000000000000000000000000000000
χ474-440-400004-4−2−2i3−2+2i32+2i32−2i3000040-4−2−2i3−2+2i32+2i32−2i30000000000000000000000000000000000000000000
χ484-440-400004-4−2+2i3−2−2i32−2i32+2i3000040-4−2+2i3−2−2i32−2i32+2i30000000000000000000000000000000000000000000
χ494-4-20200004-444-4-40000-202-2-222000000000000000−i6i600−i6i6−i6i600000000000000000000
χ504-4-20200004-444-4-40000-202-2-222000000000000000i6−i600i6−i6i6−i600000000000000000000
χ514-4-20200004-4−2−2i3−2+2i32+2i32−2i30000-2021+i31−i3−1−i3−1+i3000000000000000−i6i600−2ζ5−ζ13+2ζ23−2ζ29+ζ31−ζ37+2ζ47−2ζ53+ζ55−ζ61+2ζ71+ζ79−ζ85+2ζ95−2ζ101+ζ103−ζ109−2ζ125+ζ127+2ζ143−2ζ149+ζ151−ζ157+2ζ1672ζ5+ζ13−2ζ23+2ζ29−ζ31+ζ37−2ζ47+2ζ53−ζ55+ζ61−2ζ71−ζ79+ζ85−2ζ95+2ζ101−ζ103+ζ109+2ζ125−ζ127−2ζ143+2ζ149−ζ151+ζ157−2ζ167ζ5+2ζ13−ζ23+ζ29−2ζ31+2ζ37−ζ47+ζ53−2ζ55+2ζ61−ζ71−2ζ79+2ζ85−ζ95+ζ101−2ζ103+2ζ109+ζ125−2ζ127−ζ143+ζ149−2ζ151+2ζ157−ζ167−ζ5−2ζ13+ζ23−ζ29+2ζ31−2ζ37+ζ47−ζ53+2ζ55−2ζ61+ζ71+2ζ79−2ζ85+ζ95−ζ101+2ζ103−2ζ109−ζ125+2ζ127+ζ143−ζ149+2ζ151−2ζ157+ζ16700000000000000000000
χ524-4-20200004-4−2−2i3−2+2i32+2i32−2i30000-2021+i31−i3−1−i3−1+i3000000000000000i6−i6002ζ5+ζ13−2ζ23+2ζ29−ζ31+ζ37−2ζ47+2ζ53−ζ55+ζ61−2ζ71−ζ79+ζ85−2ζ95+2ζ101−ζ103+ζ109+2ζ125−ζ127−2ζ143+2ζ149−ζ151+ζ157−2ζ167−2ζ5−ζ13+2ζ23−2ζ29+ζ31−ζ37+2ζ47−2ζ53+ζ55−ζ61+2ζ71+ζ79−ζ85+2ζ95−2ζ101+ζ103−ζ109−2ζ125+ζ127+2ζ143−2ζ149+ζ151−ζ157+2ζ167−ζ5−2ζ13+ζ23−ζ29+2ζ31−2ζ37+ζ47−ζ53+2ζ55−2ζ61+ζ71+2ζ79−2ζ85+ζ95−ζ101+2ζ103−2ζ109−ζ125+2ζ127+ζ143−ζ149+2ζ151−2ζ157+ζ167ζ5+2ζ13−ζ23+ζ29−2ζ31+2ζ37−ζ47+ζ53−2ζ55+2ζ61−ζ71−2ζ79+2ζ85−ζ95+ζ101−2ζ103+2ζ109+ζ125−2ζ127−ζ143+ζ149−2ζ151+2ζ157−ζ16700000000000000000000
χ534-4-20200004-4−2+2i3−2−2i32−2i32+2i30000-2021−i31+i3−1+i3−1−i3000000000000000−i6i600ζ5+2ζ13−ζ23+ζ29−2ζ31+2ζ37−ζ47+ζ53−2ζ55+2ζ61−ζ71−2ζ79+2ζ85−ζ95+ζ101−2ζ103+2ζ109+ζ125−2ζ127−ζ143+ζ149−2ζ151+2ζ157−ζ167−ζ5−2ζ13+ζ23−ζ29+2ζ31−2ζ37+ζ47−ζ53+2ζ55−2ζ61+ζ71+2ζ79−2ζ85+ζ95−ζ101+2ζ103−2ζ109−ζ125+2ζ127+ζ143−ζ149+2ζ151−2ζ157+ζ167−2ζ5−ζ13+2ζ23−2ζ29+ζ31−ζ37+2ζ47−2ζ53+ζ55−ζ61+2ζ71+ζ79−ζ85+2ζ95−2ζ101+ζ103−ζ109−2ζ125+ζ127+2ζ143−2ζ149+ζ151−ζ157+2ζ1672ζ5+ζ13−2ζ23+2ζ29−ζ31+ζ37−2ζ47+2ζ53−ζ55+ζ61−2ζ71−ζ79+ζ85−2ζ95+2ζ101−ζ103+ζ109+2ζ125−ζ127−2ζ143+2ζ149−ζ151+ζ157−2ζ16700000000000000000000
χ544-4-20200004-4−2+2i3−2−2i32−2i32+2i30000-2021−i31+i3−1+i3−1−i3000000000000000i6−i600−ζ5−2ζ13+ζ23−ζ29+2ζ31−2ζ37+ζ47−ζ53+2ζ55−2ζ61+ζ71+2ζ79−2ζ85+ζ95−ζ101+2ζ103−2ζ109−ζ125+2ζ127+ζ143−ζ149+2ζ151−2ζ157+ζ167ζ5+2ζ13−ζ23+ζ29−2ζ31+2ζ37−ζ47+ζ53−2ζ55+2ζ61−ζ71−2ζ79+2ζ85−ζ95+ζ101−2ζ103+2ζ109+ζ125−2ζ127−ζ143+ζ149−2ζ151+2ζ157−ζ1672ζ5+ζ13−2ζ23+2ζ29−ζ31+ζ37−2ζ47+2ζ53−ζ55+ζ61−2ζ71−ζ79+ζ85−2ζ95+2ζ101−ζ103+ζ109+2ζ125−ζ127−2ζ143+2ζ149−ζ151+ζ157−2ζ167−2ζ5−ζ13+2ζ23−2ζ29+ζ31−ζ37+2ζ47−2ζ53+ζ55−ζ61+2ζ71+ζ79−ζ85+2ζ95−2ζ101+ζ103−ζ109−2ζ125+ζ127+2ζ143−2ζ149+ζ151−ζ157+2ζ16700000000000000000000
χ55666666666-1-1000066-1-1-1-1-1000000-1-1-1-1-10000000000000000-1-1-100000000000000000
χ566666666-6-6-1-100006-6-1-1-1-1-100000011-1-1-1000000000000000011100000000000000000
χ5766666-6666-1-10000-6-611-1-1-1000000-1-111-1000000000000000011-100000000000000000
χ5866666-66-6-6-1-10000-6611-1-1-10000001111-10000000000000000-1-1100000000000000000
χ59666-660-66-6-1-1000000−i7i7-11-1000000-1-1−i7i710000000000000000−i7i7100000000000000000
χ60666-660-66-6-1-1000000i7−i7-11-1000000-1-1i7−i710000000000000000i7−i7100000000000000000
χ61666-660-6-66-1-1000000−i7i7-11-100000011−i7i710000000000000000i7−i7-100000000000000000
χ62666-660-6-66-1-1000000i7−i7-11-100000011i7−i710000000000000000−i7i7-100000000000000000
χ631212-612-612-600-2-20000-60-2-21-2100000000111000000000000000000000000000000000000
χ641212-612-6-12-600-2-2000060221-2100000000-1-11000000000000000000000000000000000000
χ651212-6-12-60600-2-2000000−2i72i712100000000i7−i7-1000000000000000000000000000000000000
χ661212-6-12-60600-2-20000002i7−2i712100000000−i7i7-1000000000000000000000000000000000000
χ6712-12120-120000-2200000000-202000000−2i72i7000000000000000000000000000000000000000
χ6812-12120-120000-2200000000-2020000002i7−2i7000000000000000000000000000000000000000
χ6924-24-120120000-440000000020-200000000000000000000000000000000000000000000000

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