Finite Group Databasebeta

← Group #100708

Character table — Group #100708

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size111111112222444444444488888888888888888888816161616161616161616161616163232
order12222222444444444444444444488888888888888884488888888888844
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1
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
χ511111111111111111111111-1-1-1-11111-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1
χ611111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111
χ711111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-111
χ811111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ911111111-1-1-1-1111-1-1-1-1-1-11111-1-1ii−i−iii−i−iiiii−i−i−i−i1-1i−ii−iii−i−i11-1-11-1
χ1011111111-1-1-1-1111-1-1-1-1-1-11111-1-1ii−i−iii−i−i−i−i−i−iiiii1-1i−ii−i−i−iii-1-111-11
χ1111111111-1-1-1-1111-1-1-1-1-1-11111-1-1−i−iii−i−iiiiiii−i−i−i−i1-1−ii−iiii−i−i-1-111-11
χ1211111111-1-1-1-1111-1-1-1-1-1-11111-1-1−i−iii−i−iii−i−i−i−iiiii1-1−ii−ii−i−iii11-1-11-1
χ1311111111-1-1-1-1111-1-1-1-1-1-111-1-111ii−i−i−i−iiiiiii−i−i−i−i-11i−i−ii−i−iii11-1-1-11
χ1411111111-1-1-1-1111-1-1-1-1-1-111-1-111ii−i−i−i−iii−i−i−i−iiiii-11i−i−iiii−i−i-1-1111-1
χ1511111111-1-1-1-1111-1-1-1-1-1-111-1-111−i−iiiii−i−iiiii−i−i−i−i-11−iii−i−i−iii-1-1111-1
χ1611111111-1-1-1-1111-1-1-1-1-1-111-1-111−i−iiiii−i−i−i−i−i−iiiii-11−iii−iii−i−i11-1-1-11
χ1722222222222222-2-2-2-2-222-2-20000222200000000000000-2-2000000000000
χ1822222222222222-2-2-2-2-222-2-20000-2-2-2-20000000000000022000000000000
χ19222222222222-2-2222-2-2-2-22-222220000000000000000-2-200000000000000
χ20222222222222-2-2222-2-2-2-22-2-2-2-2-200000000000000002200000000000000
χ21222222222222-2-2-2-2-222-2-2-22000000002222000000000000-2-20000000000
χ22222222222222-2-2-2-2-222-2-2-2200000000-2-2-2-2000000000000220000000000
χ2322222222-2-2-2-222-22222-2-2-2-200002i2i−2i−2i00000000000000−2i2i000000000000
χ2422222222-2-2-2-222-22222-2-2-2-20000−2i−2i2i2i000000000000002i−2i000000000000
χ2522222222-2-2-2-2-2-22-2-222222-222-2-20000000000000000-2200000000000000
χ2622222222-2-2-2-2-2-22-2-222222-2-2-22200000000000000002-200000000000000
χ2722222222-2-2-2-2-2-2-222-2-222-22000000002i2i−2i−2i000000000000−2i2i0000000000
χ2822222222-2-2-2-2-2-2-222-2-222-2200000000−2i−2i2i2i0000000000002i−2i0000000000
χ2922-22-2-2-222i−2i2i−2i2-2000002i−2i0000002ζ−2ζ2ζ3−2ζ300001+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000002−2i2−i200
χ3022-22-2-2-222i−2i2i−2i2-2000002i−2i0000002ζ−2ζ2ζ3−2ζ30000−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000−22−i2i200
χ3122-22-2-2-222i−2i2i−2i2-2000002i−2i000000−2ζ2ζ−2ζ32ζ300001+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000−22−i2i200
χ3222-22-2-2-222i−2i2i−2i2-2000002i−2i000000−2ζ2ζ−2ζ32ζ30000−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000002−2i2−i200
χ3322-22-2-2-22−2i2i−2i2i2-200000−2i2i0000002ζ3−2ζ32ζ−2ζ00001−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000−22i2−i200
χ3422-22-2-2-22−2i2i−2i2i2-200000−2i2i0000002ζ3−2ζ32ζ−2ζ0000−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000002−2−i2i200
χ3522-22-2-2-22−2i2i−2i2i2-200000−2i2i000000−2ζ32ζ3−2ζ2ζ00001−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000002−2−i2i200
χ3622-22-2-2-22−2i2i−2i2i2-200000−2i2i000000−2ζ32ζ3−2ζ2ζ0000−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000−22i2−i200
χ372-2-2-22-22222-2-200-22-20000202-22-200000000i2−i2i2−i2i2−i2i2−i2000000i2−i2i2−i2000000
χ382-2-2-22-22222-2-200-22-20000202-22-200000000−i2i2−i2i2−i2i2−i2i2000000−i2i2−i2i2000000
χ392-2-2-22-22222-2-200-22-2000020-22-2200000000i2−i2i2−i2i2−i2i2−i2000000−i2i2−i2i2000000
χ402-2-2-22-22222-2-200-22-2000020-22-2200000000−i2i2−i2i2−i2i2−i2i2000000i2−i2i2−i2000000
χ412-2-2-22-222-2-22200-2-220000202-2-22000000002−22−2−22−220000002−2−22000000
χ422-2-2-22-222-2-22200-2-220000202-2-2200000000−22−222−22−2000000−222−2000000
χ432-2-2-22-222-2-22200-2-22000020-222-2000000002−22−2−22−22000000−222−2000000
χ442-2-2-22-222-2-22200-2-22000020-222-200000000−22−222−22−20000002−2−22000000
χ4544-44-4-4-444i−4i4i−4i-4400000−4i4i00000000000000000000000000000000000000
χ4644-44-4-4-44−4i4i−4i4i-44000004i−4i00000000000000000000000000000000000000
χ474-44-4-44-444i−4i−4i4i000000000000000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ0000000000000000
χ484-44-4-44-444i−4i−4i4i00000000000000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ0000000000000000
χ494-44-4-44-44−4i4i4i−4i000000000000000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ30000000000000000
χ504-44-4-44-44−4i4i4i−4i00000000000000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ30000000000000000
χ514-4-44-444-40000000004i−4i0000000000002+2i−2−2i2−2i−2+2i000000000000000000000000
χ524-4-44-444-40000000004i−4i000000000000−2−2i2+2i−2+2i2−2i000000000000000000000000
χ534-4-44-444-4000000000−4i4i0000000000002−2i−2+2i2+2i−2−2i000000000000000000000000
χ544-4-44-444-4000000000−4i4i000000000000−2+2i2−2i−2−2i2+2i000000000000000000000000
χ554-4-4-44-44444-4-4004-440000-40000000000000000000000000000000000000
χ564-4-4-44-444-4-4440044-40000-40000000000000000000000000000000000000
χ57888-8-8-88-8000000000000000000000000000000000000000000000000000
χ5888-8-888-8-8000000000000000000000000000000000000000000000000000
χ598-8888-8-8-8000000000000000000000000000000000000000000000000000

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