Finite Group Databasebeta

← Group #100656

Character table — Group #100656

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
χ3111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1
χ4111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
χ511111111111111111111111-1-1-1-11111-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1
χ611111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111
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
χ911111111-1-1-1-111-1-1-1-111-1-1111-1-1ii−i−iii−i−iiiii−i−i−i−i1-1i−ii−i11-1-1ii−i−i1-1
χ1011111111-1-1-1-111-1-1-1-111-1-1111-1-1ii−i−iii−i−i−i−i−i−iiiii1-1i−ii−i-1-111−i−iii-11
χ1111111111-1-1-1-111-1-1-1-111-1-1111-1-1−i−iii−i−iiiiiii−i−i−i−i1-1−ii−ii-1-111ii−i−i-11
χ1211111111-1-1-1-111-1-1-1-111-1-1111-1-1−i−iii−i−iii−i−i−i−iiiii1-1−ii−ii11-1-1−i−iii1-1
χ1311111111-1-1-1-111-1-1-1-111-1-11-1-111ii−i−i−i−iiiiiii−i−i−i−i-11i−i−ii11-1-1−i−iii-11
χ1411111111-1-1-1-111-1-1-1-111-1-11-1-111ii−i−i−i−iii−i−i−i−iiiii-11i−i−ii-1-111ii−i−i1-1
χ1511111111-1-1-1-111-1-1-1-111-1-11-1-111−i−iiiii−i−iiiii−i−i−i−i-11−iii−i-1-111−i−iii1-1
χ1611111111-1-1-1-111-1-1-1-111-1-11-1-111−i−iiiii−i−i−i−i−i−iiiii-11−iii−i11-1-1ii−i−i-11
χ17222222222222222-2-2-2-2-22-2-20000222200000000000000-2-2000000000000
χ18222222222222222-2-2-2-2-22-2-20000-2-2-2-20000000000000022000000000000
χ19222222222222-2-2-222-222-2-2-222220000000000000000-2-200000000000000
χ20222222222222-2-2-222-222-2-2-2-2-2-2-200000000000000002200000000000000
χ21222222222222-2-2-2-2-22-2-2-222000000002222000000000000-2-20000000000
χ22222222222222-2-2-2-2-22-2-2-22200000000-2-2-2-2000000000000220000000000
χ2322222222-2-2-2-222-2222-2-2-22-200002i2i−2i−2i00000000000000−2i2i000000000000
χ2422222222-2-2-2-222-2222-2-2-22-20000−2i−2i2i2i000000000000002i−2i000000000000
χ2522222222-2-2-2-2-2-2222-2-2-22-22000000002i2i−2i−2i000000000000−2i2i0000000000
χ2622222222-2-2-2-2-2-2222-2-2-22-2200000000−2i−2i2i2i0000000000002i−2i0000000000
χ2722222222-2-2-2-2-2-22-2-222222-222-2-20000000000000000-2200000000000000
χ2822222222-2-2-2-2-2-22-2-222222-2-2-22200000000000000002-200000000000000
χ2922-2-222-2-222-2-22-2-20000020000002i−2i2i−2i000022−2−222−2−2000000i2−i2i2−i2000000
χ3022-2-222-2-222-2-22-2-20000020000002i−2i2i−2i0000−2−222−2−222000000−i2i2−i2i2000000
χ3122-2-222-2-222-2-22-2-2000002000000−2i2i−2i2i000022−2−222−2−2000000−i2i2−i2i2000000
χ3222-2-222-2-222-2-22-2-2000002000000−2i2i−2i2i0000−2−222−2−222000000i2−i2i2−i2000000
χ3322-2-222-2-2-2-2222-2200000-20000002-2-220000i2i2−i2−i2−i2−i2i2i2000000−i2i2i2−i2000000
χ3422-2-222-2-2-2-2222-2200000-20000002-2-220000−i2−i2i2i2i2i2−i2−i2000000i2−i2−i2i2000000
χ3522-2-222-2-2-2-2222-2200000-2000000-222-20000i2i2−i2−i2−i2−i2i2i2000000i2−i2−i2i2000000
χ3622-2-222-2-2-2-2222-2200000-2000000-222-20000−i2−i2i2i2i2i2−i2−i2000000−i2i2i2−i2000000
χ372-22-22-22-22i−2i2i−2i0002i−2i02-20002-22i−2i000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000001+i−1−i1−i−1+i00
χ382-22-22-22-22i−2i2i−2i0002i−2i02-20002-22i−2i00000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000−1−i1+i−1+i1−i00
χ392-22-22-22-22i−2i2i−2i0002i−2i02-2000-22−2i2i000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000−1−i1+i−1+i1−i00
χ402-22-22-22-22i−2i2i−2i0002i−2i02-2000-22−2i2i00000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000001+i−1−i1−i−1+i00
χ412-22-22-22-2−2i2i−2i2i000−2i2i02-20002-2−2i2i000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000001−i−1+i1+i−1−i00
χ422-22-22-22-2−2i2i−2i2i000−2i2i02-20002-2−2i2i00000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000−1+i1−i−1−i1+i00
χ432-22-22-22-2−2i2i−2i2i000−2i2i02-2000-222i−2i000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000−1+i1−i−1−i1+i00
χ442-22-22-22-2−2i2i−2i2i000−2i2i02-2000-222i−2i00000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000001−i−1+i1+i−1−i00
χ4544-4-444-4-444-4-4-44400000-400000000000000000000000000000000000000
χ4644-4-444-4-4-4-444-44-400000400000000000000000000000000000000000000
χ474-44-44-44-44i−4i4i−4i000−4i4i0-44000000000000000000000000000000000000000
χ484-44-44-44-4−4i4i−4i4i0004i−4i0-44000000000000000000000000000000000000000
χ494-4-444-4-444i−4i−4i4i000000000000000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ30000000000000000
χ504-4-444-4-444i−4i−4i4i00000000000000000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ30000000000000000
χ514-4-444-4-44−4i4i4i−4i000000000000000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ0000000000000000
χ524-4-444-4-44−4i4i4i−4i00000000000000000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ0000000000000000
χ534-4-4-4-44440000000004000-40000000002i2−2i22i2−2i2000000000000000000000000
χ544-4-4-4-44440000000004000-4000000000−2i22i2−2i22i2000000000000000000000000
χ554-4-4-4-4444000000000-4000400000000022−22−2222000000000000000000000000
χ564-4-4-4-4444000000000-40004000000000−222222−22000000000000000000000000
χ57888-8-8-8-88000000000000000000000000000000000000000000000000000
χ5888-88-8-88-8000000000000000000000000000000000000000000000000000
χ598-888-88-8-8000000000000000000000000000000000000000000000000000

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