Finite Group Databasebeta

← Group #98124

Character table — Group #98124

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47
size111111114444444488816161616161616161616161616161616161616161616161616161616
order12222222444444444442224444444448888888888888888
χ111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111-1-1-1-1-1-1-111-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111-1-111-111-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111-1-111-111-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111-1-1-1-11-1-111-1-111111-1-1-1-1-1-1-1-11111
χ81111111111111111111-1-1-1-11-1-111-1-11-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-11111-1111-1-11-11-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011111111-1-1-1-1-1-1-1-11111-1111-1-11-11-1-1−i−iii−i−iii−i−iii−i−iii
χ1111111111-1-1-1-1-1-1-1-11111-1-1-1-111-111-11ii−i−iii−i−i−i−iii−i−iii
χ1211111111-1-1-1-1-1-1-1-11111-1-1-1-111-111-11−i−iii−i−iiiii−i−iii−i−i
χ1311111111-1-1-1-1-1-1-1-1111-1111-1-1-1-11-111ii−i−i−i−iiiii−i−i−i−iii
χ1411111111-1-1-1-1-1-1-1-1111-1111-1-1-1-11-111−i−iiiii−i−i−i−iiiii−i−i
χ1511111111-1-1-1-1-1-1-1-1111-11-1-11111-1-11-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111111-1-1-1-1-1-1-1-1111-11-1-11111-1-11-1−i−iiiii−i−iii−i−i−i−iii
χ172222222222-2-2-2-2222-2-2220000000-2-200000000000000000
χ182222222222-2-2-2-2222-2-2-2-200000002200000000000000000
χ19222222222-222-2-22-2-22-20000200-2-20020000000000000000
χ20222222222-222-2-22-2-22-20000-2002200-20000000000000000
χ21222222222-2-2-2222-2-2-22002-202-2000000000000000000000
χ22222222222-2-2-2222-2-2-2200-220-22000000000000000000000
χ2322222222-2222-2-2-22-2-22002-20-22000000000000000000000
χ2422222222-2222-2-2-22-2-2200-2202-2000000000000000000000
χ2522222222-22-2-222-22-22-20000200-2200-20000000000000000
χ2622222222-22-2-222-22-22-20000-2002-20020000000000000000
χ2722222222-2-22222-2-22-2-22-20000000-2200000000000000000
χ2822222222-2-22222-2-22-2-2-2200000002-200000000000000000
χ2944-44-44-4-400004i−4i00000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ3044-44-44-4-400004i−4i0000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ3144-44-44-4-40000−4i4i00000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ3244-44-44-4-40000−4i4i0000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ334-444-4-44-4004i−4i00000000000000000002ζ−2ζ2ζ3−2ζ3000000000000
χ344-444-4-44-4004i−4i0000000000000000000−2ζ2ζ−2ζ32ζ3000000000000
χ354-444-4-44-400−4i4i00000000000000000002ζ3−2ζ32ζ−2ζ000000000000
χ364-444-4-44-400−4i4i0000000000000000000−2ζ32ζ3−2ζ2ζ000000000000
χ374-44-4-44-440400000-40000000000000000000000000002i−2i2i−2i
χ384-44-4-44-440400000-4000000000000000000000000000−2i2i−2i2i
χ394-44-4-44-440-40000040000000000000000000000000002-2-22
χ404-44-4-44-440-4000004000000000000000000000000000-222-2
χ414-4-4-4444-4400000-4000000000000000000002i−2i2i−2i00000000
χ424-4-4-4444-4400000-400000000000000000000−2i2i−2i2i00000000
χ434-4-4-4444-4-4000004000000000000000000002-2-2200000000
χ444-4-4-4444-4-400000400000000000000000000-222-200000000
χ45888-88-8-8-8000000000000000000000000000000000000000
χ4688-8-8-8-888000000000000000000000000000000000000000
χ478-8-888-8-88000000000000000000000000000000000000000

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