Finite Group Databasebeta

← Group #11784082

Character table — Group #11784082

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11112222224444444444448888888888889999999999991616161616161616181818181818181818181818181818181818363636363636363636363636
order1222448888223344666666121212122424242424242424444488888888666612121212224444444488888888444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1iiii−i−i−i−i11111111-1-1iiii−i−i−i−i-1-1-1-1ii−i−i-1-1-1-1ii−i−iii−i−i
χ41111111111111111111111111111111111-1-1-1-1−i−i−i−iiiii11111111-1-1−i−i−i−iiiii-1-1-1-1−i−iii-1-1-1-1−i−iii−i−iii
χ51111111111-1-111-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ61111111111-1-111-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ71111111111-1-111-1-1111111111111111111-1-1-1-1iiii−i−i−i−i-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-1-1-1ii−i−i1111−i−iii−i−iii
χ81111111111-1-111-1-1111111111111111111-1-1-1-1−i−i−i−iiiii-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-1-1-1−i−iii1111ii−i−iii−i−i
χ9111111-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111
χ10111111-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ11111111-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i1111-1-1-1-1-1-1−i−i−i−iiiii1111ii−i−i11-1-1−i−iiiii−i−i
χ12111111-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii1111-1-1-1-1-1-1iiii−i−i−i−i1111−i−iii11-1-1ii−i−i−i−iii
χ13111111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1
χ14111111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111
χ15111111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-1-1-11111-1-1−i−i−i−iiiii1111ii−i−i-1-111ii−i−i−i−iii
χ16111111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-1-1-11111-1-1iiii−i−i−i−i1111−i−iii-1-111−i−iiiii−i−i
χ171-1-111-1ii−i−i1-111i−i-1-111-1-111-1-1iiii−i−i−i−i11-1-1ii−i−iii−i−i11-1-1ii−i−i-1111-1-111-1-1ii−i−ii−ii−ii−i1-11-11-1i−ii−i
χ181-1-111-1ii−i−i1-111i−i-1-111-1-111-1-1iiii−i−i−i−i11-1-1−i−iii−i−iii11-1-1ii−i−i-11-1-111-1-111ii−i−i−ii−iii−i1-1-11-11−ii−ii
χ191-1-111-1ii−i−i1-111i−i-1-111-1-111-1-1iiii−i−i−i−i-1-11111-1-1-1-11111-1-1ii−i−i1-1−i−iiiii−i−i−i−iii1-1-11−ii-11−iii−i1-1-11
χ201-1-111-1ii−i−i1-111i−i-1-111-1-111-1-1iiii−i−i−i−i-1-111-1-11111-1-111-1-1ii−i−i1-1ii−i−i−i−iii−i−iii-111-1−ii-11i−i−ii-111-1
χ211-1-111-1ii−i−i-1111−ii-1-111-1-111-1-1iiii−i−i−i−i11-1-1ii−i−iii−i−i-1-111−i−iii-1111-1-111-1-1ii−i−ii−ii−i−ii-11-11-11−ii−ii
χ221-1-111-1ii−i−i-1111−ii-1-111-1-111-1-1iiii−i−i−i−i11-1-1−i−iii−i−iii-1-111−i−iii-11-1-111-1-111ii−i−i−ii−ii−ii-111-11-1i−ii−i
χ231-1-111-1ii−i−i-1111−ii-1-111-1-111-1-1iiii−i−i−i−i-1-11111-1-1-1-111-1-111−i−iii1-1−i−iiiii−i−i−i−iii1-1-11i−i1-1i−i−ii-111-1
χ241-1-111-1ii−i−i-1111−ii-1-111-1-111-1-1iiii−i−i−i−i-1-111-1-11111-1-1-1-111−i−iii1-1ii−i−i−i−iii−i−iii-111-1i−i1-1−iii−i1-1-11
χ251-1-111-1−i−iii1-111−ii-1-111-1-111-1-1−i−i−i−iiiii11-1-1ii−i−iii−i−i11-1-1−i−iii-11-1-111-1-111−i−iiii−ii−i−ii1-1-11-11i−ii−i
χ261-1-111-1−i−iii1-111−ii-1-111-1-111-1-1−i−i−i−iiiii11-1-1−i−iii−i−iii11-1-1−i−iii-1111-1-111-1-1−i−iii−ii−ii−ii1-11-11-1−ii−ii
χ271-1-111-1−i−iii1-111−ii-1-111-1-111-1-1−i−i−i−iiiii-1-11111-1-1-1-11111-1-1−i−iii1-1ii−i−i−i−iiiii−i−i1-1-11i−i-11i−i−ii1-1-11
χ281-1-111-1−i−iii1-111−ii-1-111-1-111-1-1−i−i−i−iiiii-1-111-1-11111-1-111-1-1−i−iii1-1−i−iiiii−i−iii−i−i-111-1i−i-11−iii−i-111-1
χ291-1-111-1−i−iii-1111i−i-1-111-1-111-1-1−i−i−i−iiiii11-1-1ii−i−iii−i−i-1-111ii−i−i-11-1-111-1-111−i−iiii−ii−ii−i-111-11-1−ii−ii
χ301-1-111-1−i−iii-1111i−i-1-111-1-111-1-1−i−i−i−iiiii11-1-1−i−iii−i−iii-1-111ii−i−i-1111-1-111-1-1−i−iii−ii−iii−i-11-11-11i−ii−i
χ311-1-111-1−i−iii-1111i−i-1-111-1-111-1-1−i−i−i−iiiii-1-11111-1-1-1-111-1-111ii−i−i1-1ii−i−i−i−iiiii−i−i1-1-11−ii1-1−iii−i-111-1
χ321-1-111-1−i−iii-1111i−i-1-111-1-111-1-1−i−i−i−iiiii-1-111-1-11111-1-1-1-111ii−i−i1-1−i−iiiii−i−iii−i−i-111-1−ii1-1i−i−ii1-1-11
χ332222-2-20000002200222222-2-2-2-20000000022222222222200000000-2-2000000000000-2-2-2-2000000000000
χ342222-2-20000002200222222-2-2-2-2000000002222-2-2-2-2-2-2-2-200000000-2-20000000000002222000000000000
χ352222-2-20000002200222222-2-2-2-200000000-2-2-2-22i2i2i2i−2i−2i−2i−2i0000000022000000000000−2i−2i2i2i000000000000
χ362222-2-20000002200222222-2-2-2-200000000-2-2-2-2−2i−2i−2i−2i2i2i2i2i00000000220000000000002i2i−2i−2i000000000000
χ3722-2-2002−22−2002200-2-2-2-222000022−2−222−2−22i−2i2i−2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000001+i−1−i1+i−1−i1−i−1+i1−i−1+ii2−i2i2−i20000000000000000
χ3822-2-2002−22−2002200-2-2-2-222000022−2−222−2−22i−2i2i−2i−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−ii2−i2i2−i20000000000000000
χ3922-2-2002−22−2002200-2-2-2-222000022−2−222−2−2−2i2i−2i2i2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−i2i2−i2i20000000000000000
χ4022-2-2002−22−2002200-2-2-2-222000022−2−222−2−2−2i2i−2i2i−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i−i2i2−i2i20000000000000000
χ4122-2-200−22−22002200-2-2-2-2220000−2−222−2−2222i−2i2i−2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i−i2i2−i2i20000000000000000
χ4222-2-200−22−22002200-2-2-2-2220000−2−222−2−2222i−2i2i−2i−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i−i2i2−i2i20000000000000000
χ4322-2-200−22−22002200-2-2-2-2220000−2−222−2−222−2i2i−2i2i2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000001−i−1+i1−i−1+i1+i−1−i1+i−1−ii2−i2i2−i20000000000000000
χ4422-2-200−22−22002200-2-2-2-2220000−2−222−2−222−2i2i−2i2i−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+ii2−i2i2−i20000000000000000
χ452-22-200i2−i2−i2i200220022-2-2-2-20000i2i2−i2−i2−i2−i2i2i22i−2i−2i2i2ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ00000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i−222−20000000000000000
χ462-22-200i2−i2−i2i200220022-2-2-2-20000i2i2−i2−i2−i2−i2i2i22i−2i−2i2i−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ0000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i−222−20000000000000000
χ472-22-200i2−i2−i2i200220022-2-2-2-20000i2i2−i2−i2−i2−i2i2i2−2i2i2i−2i2ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ300000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i2−2−220000000000000000
χ482-22-200i2−i2−i2i200220022-2-2-2-20000i2i2−i2−i2−i2−i2i2i2−2i2i2i−2i−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ30000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i2−2−220000000000000000
χ492-22-200−i2i2i2−i200220022-2-2-2-20000−i2−i2i2i2i2i2−i2−i22i−2i−2i2i2ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ0000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i2−2−220000000000000000
χ502-22-200−i2i2i2−i200220022-2-2-2-20000−i2−i2i2i2i2i2−i2−i22i−2i−2i2i−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ00000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i2−2−220000000000000000
χ512-22-200−i2i2i2−i200220022-2-2-2-20000−i2−i2i2i2i2i2−i2−i2−2i2i2i−2i2ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ30000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i−222−20000000000000000
χ522-22-200−i2i2i2−i200220022-2-2-2-20000−i2−i2i2i2i2i2−i2−i2−2i2i2i−2i−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ300000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i−222−20000000000000000
χ532-2-22-220000002200-2-222-2-2-2-2220000000022-2-22i2i−2i−2i2i2i−2i−2i000000002-2000000000000−2i2i−2i2i000000000000
χ542-2-22-220000002200-2-222-2-2-2-2220000000022-2-2−2i−2i2i2i−2i−2i2i2i000000002-20000000000002i−2i2i−2i000000000000
χ552-2-22-220000002200-2-222-2-2-2-22200000000-2-22222-2-2-2-22200000000-22000000000000-222-2000000000000
χ562-2-22-220000002200-2-222-2-2-2-22200000000-2-222-2-22222-2-200000000-220000000000002-2-22000000000000
χ574444444444441-2441-21-21-21-21-21-21-21-21-20000000000001-21-21-21-2000000000000000000000000000000
χ58444444444444-2144-21-21-21-21-21-21-21-21-21000000000000-21-21-21-21000000000000000000000000000000
χ594444444444-4-41-2-4-41-21-21-21-21-21-21-21-21-2000000000000-12-12-12-12000000000000000000000000000000
χ604444444444-4-4-21-4-4-21-21-21-21-21-21-21-21-210000000000002-12-12-12-1000000000000000000000000000000
χ61444444-4-4-4-4441-2-4-41-21-21-21-21-2-12-12-12-120000000000001-21-2-12-12000000000000000000000000000000
χ62444444-4-4-4-444-21-4-4-21-21-21-21-212-12-12-12-1000000000000-21-212-12-1000000000000000000000000000000
χ63444444-4-4-4-4-4-41-2441-21-21-21-21-2-12-12-12-12000000000000-12-121-21-2000000000000000000000000000000
χ64444444-4-4-4-4-4-4-2144-21-21-21-21-212-12-12-12-10000000000002-12-1-21-21000000000000000000000000000000
χ654-4-444-44i4i−4i−4i4-41-24i−4i-121-2-121-2-12i−2ii−2i−i2i−i2i0000000000001-2-12i−2i−i2i000000000000000000000000000000
χ664-4-444-44i4i−4i−4i4-4-214i−4i2-1-212-1-212-1−2ii−2ii2i−i2i−i000000000000-212-1−2ii2i−i000000000000000000000000000000
χ674-4-444-44i4i−4i−4i-441-2−4i4i-121-2-121-2-12i−2ii−2i−i2i−i2i000000000000-121-2−i2ii−2i000000000000000000000000000000
χ684-4-444-44i4i−4i−4i-44-21−4i4i2-1-212-1-212-1−2ii−2ii2i−i2i−i0000000000002-1-212i−i−2ii000000000000000000000000000000
χ694-4-444-4−4i−4i4i4i4-41-2−4i4i-121-2-121-2-12−i2i−i2ii−2ii−2i0000000000001-2-12−i2ii−2i000000000000000000000000000000
χ704-4-444-4−4i−4i4i4i4-4-21−4i4i2-1-212-1-212-12i−i2i−i−2ii−2ii000000000000-212-12i−i−2ii000000000000000000000000000000
χ714-4-444-4−4i−4i4i4i-441-24i−4i-121-2-121-2-12−i2i−i2ii−2ii−2i000000000000-121-2i−2i−i2i000000000000000000000000000000
χ724-4-444-4−4i−4i4i4i-44-214i−4i2-1-212-1-212-12i−i2i−i−2ii−2ii0000000000002-1-21−2ii2i−i000000000000000000000000000000
χ738888-8-80000002-4002-42-42-4-24-240000000000000000000000000000000000000000000000000000000000
χ748888-8-8000000-4200-42-42-424-24-20000000000000000000000000000000000000000000000000000000000
χ7588-8-80042−4242−42002-400-24-242-400002−22−2222−22−22200000000000000000000000000000000000000000000000000
χ7688-8-80042−4242−4200-42004-24-2-420000−22222−2−22222−200000000000000000000000000000000000000000000000000
χ7788-8-800−4242−4242002-400-24-242-40000−2222−22−2222−2200000000000000000000000000000000000000000000000000
χ7888-8-800−4242−424200-42004-24-2-42000022−2−22222−2−22200000000000000000000000000000000000000000000000000
χ798-88-8004i2−4i2−4i24i2002-4002-4-24-240000i2−2i2−i22i2−i22i2i2−2i200000000000000000000000000000000000000000000000000
χ808-88-8004i2−4i2−4i24i200-4200-424-24-20000−2i2i22i2−i22i2−i2−2i2i200000000000000000000000000000000000000000000000000
χ818-88-800−4i24i24i2−4i2002-4002-4-24-240000−i22i2i2−2i2i2−2i2−i22i200000000000000000000000000000000000000000000000000
χ828-88-800−4i24i24i2−4i200-4200-424-24-200002i2−i2−2i2i2−2i2i22i2−i200000000000000000000000000000000000000000000000000
χ838-8-88-880000002-400-242-4-24-242-40000000000000000000000000000000000000000000000000000000000
χ848-8-88-88000000-42004-2-424-24-2-420000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.