Finite Group Databasebeta

← Group #101652

Character table — Group #101652

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111111112222444444448888888888888816161616161616161616161616161616161616161616
order12222222444422444444444444888888884444448888888888888888
χ111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111111-1-1-1-1111111-1-1-1-1-111-11111-1-1-1-1-1-1-1-1-1-11111
χ611111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1
χ711111111111111111111-1-1-1-111-1-1-1-11111-111-111-1-1111111-1-1-1-1-1-1-1-1
χ811111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111111
χ911111111-1-1-1-1111-1-1-11-111-1-11-1ii−i−iii−i−i111-1-1-1i−ii−iii−i−i11-1-1ii−i−i
χ1011111111-1-1-1-1111-1-1-11-111-1-11-1ii−i−iii−i−i1-1-1-111i−ii−i−i−iii-1-111−i−iii
χ1111111111-1-1-1-1111-1-1-11-111-1-11-1−i−iii−i−iii111-1-1-1−ii−ii−i−iii11-1-1−i−iii
χ1211111111-1-1-1-1111-1-1-11-111-1-11-1−i−iii−i−iii1-1-1-111−ii−iiii−i−i-1-111ii−i−i
χ1311111111-1-1-1-1111-1-1-11-1-1-1111-1ii−i−i−i−iii-1111-1-1i−i−ii−i−iii-1-111ii−i−i
χ1411111111-1-1-1-1111-1-1-11-1-1-1111-1ii−i−i−i−iii-1-1-1111i−i−iiii−i−i11-1-1−i−iii
χ1511111111-1-1-1-1111-1-1-11-1-1-1111-1−i−iiiii−i−i-1111-1-1−iii−iii−i−i-1-111−i−iii
χ1611111111-1-1-1-1111-1-1-11-1-1-1111-1−i−iiiii−i−i-1-1-1111−iii−i−i−iii11-1-1ii−i−i
χ1722222222222222-2-222-2-20000-2-20000222200000000-2-2000000000000
χ1822222222222222-2-222-2-20000-2-20000-2-2-2-20000000022000000000000
χ19222222222222-2-22-2-2-22-22222-2200000000-200-2000000000000000000
χ20222222222222-2-22-2-2-22-2-2-2-2-2-22000000002002000000000000000000
χ21222222222222-2-2-22-2-2-2200002-222220000000000-2-200000000000000
χ22222222222222-2-2-22-2-2-2200002-2-2-2-2-200000000002200000000000000
χ2322222222-2-2-2-222-22-2-2-220000-2200002i2i−2i−2i00000000−2i2i000000000000
χ2422222222-2-2-2-222-22-2-2-220000-220000−2i−2i2i2i000000002i−2i000000000000
χ2522222222-2-2-2-2-2-222222222-2-2-2-200000000-2002000000000000000000
χ2622222222-2-2-2-2-2-2222222-2-222-2-200000000200-2000000000000000000
χ2722222222-2-2-2-2-2-2-2-222-2-20000222i2i−2i−2i0000000000−2i2i00000000000000
χ2822222222-2-2-2-2-2-2-2-222-2-2000022−2i−2i2i2i00000000002i−2i00000000000000
χ29222-2-2-2-222i−2i2i−2i2-2002i−2i0000000000002ζ3−2ζ32ζ−2ζ000000000000002−2i2−i21−i−1+i1+i−1−i
χ30222-2-2-2-222i−2i2i−2i2-2002i−2i0000000000002ζ3−2ζ32ζ−2ζ00000000000000−22−i2i2−1+i1−i−1−i1+i
χ31222-2-2-2-222i−2i2i−2i2-2002i−2i000000000000−2ζ32ζ3−2ζ2ζ000000000000002−2i2−i2−1+i1−i−1−i1+i
χ32222-2-2-2-222i−2i2i−2i2-2002i−2i000000000000−2ζ32ζ3−2ζ2ζ00000000000000−22−i2i21−i−1+i1+i−1−i
χ33222-2-2-2-22−2i2i−2i2i2-200−2i2i0000000000002ζ−2ζ2ζ3−2ζ3000000000000002−2−i2i2−1−i1+i−1+i1−i
χ34222-2-2-2-22−2i2i−2i2i2-200−2i2i0000000000002ζ−2ζ2ζ3−2ζ300000000000000−22i2−i21+i−1−i1−i−1+i
χ35222-2-2-2-22−2i2i−2i2i2-200−2i2i000000000000−2ζ2ζ−2ζ32ζ3000000000000002−2−i2i21+i−1−i1−i−1+i
χ36222-2-2-2-22−2i2i−2i2i2-200−2i2i000000000000−2ζ2ζ−2ζ32ζ300000000000000−22i2−i2−1−i1+i−1+i1−i
χ37444-4-4-4-444i−4i4i−4i-4400−4i4i00000000000000000000000000000000000000
χ38444-4-4-4-44−4i4i−4i4i-44004i−4i00000000000000000000000000000000000000
χ3944-44-44-4-40000004000-404-40000000000000000000000000000000000
χ4044-44-44-4-40000004000-40-440000000000000000000000000000000000
χ4144-44-44-4-4000000-400040004i−4i00000000000000000000000000000000
χ4244-44-44-4-4000000-40004000−4i4i00000000000000000000000000000000
χ434-4444-4-4-444-4-4000000000000000000000000000000002-22-200000000
χ444-4444-4-4-444-4-400000000000000000000000000000000-22-2200000000
χ454-4444-4-4-4-4-444000000000000000000000000000000002i−2i−2i2i00000000
χ464-4444-4-4-4-4-44400000000000000000000000000000000−2i2i2i−2i00000000
χ474-44-4-444-44i−4i−4i4i000000000000000000000002-202i−2i0000000000000000
χ484-44-4-444-44i−4i−4i4i00000000000000000000000-220−2i2i0000000000000000
χ494-44-4-444-4−4i4i4i−4i000000000000000000000002-20−2i2i0000000000000000
χ504-44-4-444-4−4i4i4i−4i00000000000000000000000-2202i−2i0000000000000000
χ514-4-44-4-44400000004000-40000002i2−2i22i2−2i200000000000000000000000000
χ524-4-44-4-44400000004000-4000000−2i22i2−2i22i200000000000000000000000000
χ534-4-44-4-4440000000-4000400000022−22−222200000000000000000000000000
χ544-4-44-4-4440000000-40004000000−222222−2200000000000000000000000000
χ5588-8-88-88-8000000000000000000000000000000000000000000000000
χ568-8-8-888-88000000000000000000000000000000000000000000000000

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