Finite Group Databasebeta

← Group #100690

Character table — Group #100690

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size111111112222444444444488888888888888888888816161616161616161616161616163232
order12222222444422444444444444488888888888888884488888888888844
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
χ911111111-1-1-1-1-1-1111-1-1-11-1111-1-1ii−i−iii−i−iiiii−i−i−i−i1-1i−ii−iii−i−i11-1-11-1
χ1011111111-1-1-1-1-1-1111-1-1-11-1111-1-1ii−i−iii−i−i−i−i−i−iiiii1-1i−ii−i−i−iii-1-111-11
χ1111111111-1-1-1-1-1-1111-1-1-11-1111-1-1−i−iii−i−iiiiiii−i−i−i−i1-1−ii−iiii−i−i-1-111-11
χ1211111111-1-1-1-1-1-1111-1-1-11-1111-1-1−i−iii−i−iii−i−i−i−iiiii1-1−ii−ii−i−iii11-1-11-1
χ1311111111-1-1-1-1-1-1111-1-1-11-11-1-111ii−i−i−i−iiiiiii−i−i−i−i-11i−i−ii−i−iii11-1-1-11
χ1411111111-1-1-1-1-1-1111-1-1-11-11-1-111ii−i−i−i−iii−i−i−i−iiiii-11i−i−iiii−i−i-1-1111-1
χ1511111111-1-1-1-1-1-1111-1-1-11-11-1-111−i−iiiii−i−iiiii−i−i−i−i-11−iii−i−i−iii-1-1111-1
χ1611111111-1-1-1-1-1-1111-1-1-11-11-1-111−i−iiiii−i−i−i−i−i−iiiii-11−iii−iii−i−i11-1-1-11
χ17222222222222222-2-2-2-2-22-2-222220000000000000000-2-200000000000000
χ18222222222222222-2-2-2-2-22-2-2-2-2-2-200000000000000002200000000000000
χ19222222222222-2-2-222-222-2-2-20000222200000000000000-2-2000000000000
χ20222222222222-2-2-222-222-2-2-20000-2-2-2-20000000000000022000000000000
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
χ2522222222-2-2-2-222-2-2-2-222-2-22000000002i2i−2i−2i000000000000−2i2i0000000000
χ2622222222-2-2-2-222-2-2-2-222-2-2200000000−2i−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
χ29222-2-2-2-222i2i−2i−2i0002-202i−2i00000002ζ−2ζ2ζ3−2ζ300001+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000002−2i2−i200
χ30222-2-2-2-222i2i−2i−2i0002-202i−2i00000002ζ−2ζ2ζ3−2ζ30000−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000−22−i2i200
χ31222-2-2-2-222i2i−2i−2i0002-202i−2i0000000−2ζ2ζ−2ζ32ζ300001+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000−22−i2i200
χ32222-2-2-2-222i2i−2i−2i0002-202i−2i0000000−2ζ2ζ−2ζ32ζ30000−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000002−2i2−i200
χ33222-2-2-2-22−2i−2i2i2i0002-20−2i2i00000002ζ3−2ζ32ζ−2ζ00001−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000−22i2−i200
χ34222-2-2-2-22−2i−2i2i2i0002-20−2i2i00000002ζ3−2ζ32ζ−2ζ0000−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000002−2−i2i200
χ35222-2-2-2-22−2i−2i2i2i0002-20−2i2i0000000−2ζ32ζ3−2ζ2ζ00001−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000002−2−i2i200
χ36222-2-2-2-22−2i−2i2i2i0002-20−2i2i0000000−2ζ32ζ3−2ζ2ζ0000−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000−22i2−i200
χ372-2222-2-2-22-22-22-2-2000002002i−2i2i−2i000000002−22−22−22−2000000i2−i2i2−i2000000
χ382-2222-2-2-22-22-22-2-2000002002i−2i2i−2i00000000−22−22−22−22000000−i2i2−i2i2000000
χ392-2222-2-2-22-22-22-2-200000200−2i2i−2i2i000000002−22−22−22−2000000−i2i2−i2i2000000
χ402-2222-2-2-22-22-22-2-200000200−2i2i−2i2i00000000−22−22−22−22000000i2−i2i2−i2000000
χ412-2222-2-2-2-22-22-22-2000002002i−2i−2i2i00000000i2−i2i2−i2−i2i2−i2i2000000−222−2000000
χ422-2222-2-2-2-22-22-22-2000002002i−2i−2i2i00000000−i2i2−i2i2i2−i2i2−i20000002−2−22000000
χ432-2222-2-2-2-22-22-22-200000200−2i2i2i−2i00000000i2−i2i2−i2−i2i2−i2i20000002−2−22000000
χ442-2222-2-2-2-22-22-22-200000200−2i2i2i−2i00000000−i2i2−i2i2i2−i2i2−i2000000−222−2000000
χ45444-4-4-4-444i4i−4i−4i000-440−4i4i000000000000000000000000000000000000000
χ46444-4-4-4-44−4i−4i4i4i000-4404i−4i000000000000000000000000000000000000000
χ474-4444-4-4-44-44-4-44400000-400000000000000000000000000000000000000
χ484-4444-4-4-4-44-444-4400000-400000000000000000000000000000000000000
χ494-44-4-444-44i−4i−4i4i000000000000000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ30000000000000000
χ504-44-4-444-44i−4i−4i4i00000000000000000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ30000000000000000
χ514-44-4-444-4−4i4i4i−4i000000000000000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ0000000000000000
χ524-44-4-444-4−4i4i4i−4i00000000000000000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ0000000000000000
χ534-4-44-44-440000000004000-40000000002i2−2i22i2−2i2000000000000000000000000
χ544-4-44-44-440000000004000-4000000000−2i22i2−2i22i2000000000000000000000000
χ554-4-44-44-44000000000-4000400000000022−22−2222000000000000000000000000
χ564-4-44-44-44000000000-40004000000000−222222−22000000000000000000000000
χ5788-88-8-88-8000000000000000000000000000000000000000000000000000
χ5888-8-888-8-8000000000000000000000000000000000000000000000000000
χ598-8-8-88-888000000000000000000000000000000000000000000000000000

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