Finite Group Databasebeta

← Group #100676

Character table — Group #100676

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size111111112222444444444488888888888888888888816161616161616161616161616163232
order12222222444422444444444444488888888888888882444448888888844
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111
χ511111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-1
χ611111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111
χ711111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-111
χ811111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1
χ911111111-1-1-1-1-1-1-1-11111-1-1111-1-1ii−i−iii−i−iiiii−i−i−i−i1-1ii−i−ii−ii−i11-1-11-1
χ1011111111-1-1-1-1-1-1-1-11111-1-1111-1-1ii−i−iii−i−i−i−i−i−iiiii1-1−i−iiii−ii−i-1-111-11
χ1111111111-1-1-1-1-1-1-1-11111-1-1111-1-1−i−iii−i−iiiiiii−i−i−i−i1-1ii−i−i−ii−ii-1-111-11
χ1211111111-1-1-1-1-1-1-1-11111-1-1111-1-1−i−iii−i−iii−i−i−i−iiiii1-1−i−iii−ii−ii11-1-11-1
χ1311111111-1-1-1-1-1-1-1-11111-1-11-1-111ii−i−i−i−iiiiiii−i−i−i−i-11−i−iiii−i−ii11-1-1-11
χ1411111111-1-1-1-1-1-1-1-11111-1-11-1-111ii−i−i−i−iii−i−i−i−iiiii-11ii−i−ii−i−ii-1-1111-1
χ1511111111-1-1-1-1-1-1-1-11111-1-11-1-111−i−iiiii−i−iiiii−i−i−i−i-11−i−iii−iii−i-1-1111-1
χ1611111111-1-1-1-1-1-1-1-11111-1-11-1-111−i−iiiii−i−i−i−i−i−iiiii-11ii−i−i−iii−i11-1-1-11
χ1722222222222222-2-222-2-2-2-2-200002222000000000000000000-2-200000000
χ1822222222222222-2-222-2-2-2-2-20000-2-2-2-20000000000000000002200000000
χ19222222222222-2-222-2-222-2-2-222220000000000000000-2-200000000000000
χ20222222222222-2-222-2-222-2-2-2-2-2-2-200000000000000002200000000000000
χ21222222222222-2-2-2-2-2-2-2-22220000000022220000000000000000-2-2000000
χ22222222222222-2-2-2-2-2-2-2-222200000000-2-2-2-2000000000000000022000000
χ2322222222-2-2-2-22222-2-2-2-2-2-22000000002i2i−2i−2i0000000000000000−2i2i000000
χ2422222222-2-2-2-22222-2-2-2-2-2-2200000000−2i−2i2i2i00000000000000002i−2i000000
χ2522222222-2-2-2-222-2-2-2-22222-222-2-20000000000000000-2200000000000000
χ2622222222-2-2-2-222-2-2-2-22222-2-2-22200000000000000002-200000000000000
χ2722222222-2-2-2-2-2-22222-2-222-200002i2i−2i−2i000000000000000000−2i2i00000000
χ2822222222-2-2-2-2-2-22222-2-222-20000−2i−2i2i2i0000000000000000002i−2i00000000
χ2922-22-2-22-22i−2i2i−2i002i−2i002-20002i−2i2-2000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i001+i−1−i1−i−1+i0000000000
χ3022-22-2-22-22i−2i2i−2i002i−2i002-20002i−2i2-200000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i00−1−i1+i−1+i1−i0000000000
χ3122-22-2-22-22i−2i2i−2i002i−2i002-2000−2i2i-22000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i00−1−i1+i−1+i1−i0000000000
χ3222-22-2-22-22i−2i2i−2i002i−2i002-2000−2i2i-2200000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i001+i−1−i1−i−1+i0000000000
χ3322-22-2-22-2−2i2i−2i2i00−2i2i002-20002i−2i-22000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i00−1+i1−i−1−i1+i0000000000
χ3422-22-2-22-2−2i2i−2i2i00−2i2i002-20002i−2i-2200000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i001−i−1+i1+i−1−i0000000000
χ3522-22-2-22-2−2i2i−2i2i00−2i2i002-2000−2i2i2-2000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i001−i−1+i1+i−1−i0000000000
χ3622-22-2-22-2−2i2i−2i2i00−2i2i002-2000−2i2i2-200000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i00−1+i1−i−1−i1+i0000000000
χ372-2-2-22-22222-2-22-2002-20000000002i−2i2i−2i0000i2−i2i2−i2i2−i2i2−i200000000002−22−200
χ382-2-2-22-22222-2-22-2002-20000000002i−2i2i−2i0000−i2i2−i2i2−i2i2−i2i20000000000−22−2200
χ392-2-2-22-22222-2-22-2002-2000000000−2i2i−2i2i0000i2−i2i2−i2i2−i2i2−i20000000000−22−2200
χ402-2-2-22-22222-2-22-2002-2000000000−2i2i−2i2i0000−i2i2−i2i2−i2i2−i2i200000000002−22−200
χ412-2-2-22-222-2-222-22002-20000000002-2-2200002−22−2−22−2200000000002−2−2200
χ422-2-2-22-222-2-222-22002-20000000002-2-220000−22−222−22−20000000000−222−200
χ432-2-2-22-222-2-222-22002-2000000000-222-200002−22−2−22−220000000000−222−200
χ442-2-2-22-222-2-222-22002-2000000000-222-20000−22−222−22−200000000002−2−2200
χ45444-4-4-4-440000000000004i−4i0000000002+2i−2−2i2−2i−2+2i000000000000000000000000
χ46444-4-4-4-440000000000004i−4i000000000−2−2i2+2i−2+2i2−2i000000000000000000000000
χ47444-4-4-4-44000000000000−4i4i0000000002−2i−2+2i2+2i−2−2i000000000000000000000000
χ48444-4-4-4-44000000000000−4i4i000000000−2+2i2−2i−2−2i2+2i000000000000000000000000
χ4944-44-4-44-44i−4i4i−4i00−4i4i00-44000000000000000000000000000000000000000
χ5044-44-4-44-4−4i4i−4i4i004i−4i00-44000000000000000000000000000000000000000
χ514-44-4-444-44i−4i−4i4i000000000000000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ30000000000000000
χ524-44-4-444-44i−4i−4i4i00000000000000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ30000000000000000
χ534-44-4-444-4−4i4i4i−4i000000000000000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ0000000000000000
χ544-44-4-444-4−4i4i4i−4i00000000000000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ0000000000000000
χ554-4-4-44-44444-4-4-4400-4400000000000000000000000000000000000000000
χ564-4-4-44-444-4-4444-400-4400000000000000000000000000000000000000000
χ5788-8-888-8-8000000000000000000000000000000000000000000000000000
χ588-8888-8-8-8000000000000000000000000000000000000000000000000000
χ598-8-88-88-88000000000000000000000000000000000000000000000000000

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