Finite Group Databasebeta

← Group #98092

Character table — Group #98092

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111111112222444444448888888888888816161616161616161616161616161616161616161616
order12222222444444444444444444888888882224444444888888888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-111-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-11111111111-1-1-1-1-111-1-1-1-1-1-1-1-1-11111
χ61111111111111111111111-1-1-1-111111111-1-11-1-111-1-11-1-1-1-11111-1-1-1-1
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111-111111111-1-1-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-111111-1-1-1-11111
χ911111111-1-1-1-1-111-1-1-1-1-11111-1-1iiii−i−i−i−i1-111-11-11-1-1ii−i−iii−i−iii−i−i
χ1011111111-1-1-1-1-111-1-1-1-1-11111-1-1iiii−i−i−i−i-11-11-1-11-111ii−i−i−i−iii−i−iii
χ1111111111-1-1-1-1-111-1-1-1-1-11111-1-1−i−i−i−iiiii1-111-11-11-1-1−i−iii−i−iii−i−iii
χ1211111111-1-1-1-1-111-1-1-1-1-11111-1-1−i−i−i−iiiii-11-11-1-11-111−i−iiiii−i−iii−i−i
χ1311111111-1-1-1-1-111-1-1-1-1-111-1-111iiii−i−i−i−i1-1-1-11-111-11−i−iii−i−iiiii−i−i
χ1411111111-1-1-1-1-111-1-1-1-1-111-1-111iiii−i−i−i−i-111-111-1-11-1−i−iiiii−i−i−i−iii
χ1511111111-1-1-1-1-111-1-1-1-1-111-1-111−i−i−i−iiiii1-1-1-11-111-11ii−i−iii−i−i−i−iii
χ1611111111-1-1-1-1-111-1-1-1-1-111-1-111−i−i−i−iiiii-111-111-1-11-1ii−i−i−i−iiiii−i−i
χ172222222222222-2-2-2-2-22-2-2200000000000000200-2-2002000000000000
χ182222222222222-2-2-2-2-22-2-2200000000000000-2002200-2000000000000
χ19222222222222-2222-2-2-22-2-2222200000000000-2-200000000000000000
χ20222222222222-2222-2-2-22-2-2-2-2-2-2000000000002200000000000000000
χ21222222222222-2-2-2-222-2-22-20000000000002-200000-220000000000000
χ22222222222222-2-2-2-222-2-22-2000000000000-22000002-20000000000000
χ2322222222-2-2-2-2222-2222-2-2-222-2-200000000000-2200000000000000000
χ2422222222-2-2-2-2222-2222-2-2-2-2-222000000000002-200000000000000000
χ2522222222-2-2-2-22-2-22-2-2222-20000000000002200000-2-20000000000000
χ2622222222-2-2-2-22-2-22-2-2222-2000000000000-2-200000220000000000000
χ2722222222-2-2-2-2-2-2-2222-22-2200000000000000200-2200-2000000000000
χ2822222222-2-2-2-2-2-2-2222-22-2200000000000000-2002-2002000000000000
χ292-2-22-2-22222-2-202-22000-2002-22-20000000000000000000000i2−i2i2−i2i2−i2i2−i2
χ302-2-22-2-22222-2-202-22000-2002-22-20000000000000000000000−i2i2−i2i2−i2i2−i2i2
χ312-2-22-2-22222-2-202-22000-200-22-220000000000000000000000i2−i2i2−i2−i2i2−i2i2
χ322-2-22-2-22222-2-202-22000-200-22-220000000000000000000000−i2i2−i2i2i2−i2i2−i2
χ332-2-22-2-222-2-22202-2-20002002-2-2200000000000000000000002−2−222−2−22
χ342-2-22-2-222-2-22202-2-20002002-2-220000000000000000000000−222−2−222−2
χ352-2-22-2-222-2-22202-2-2000200-222-200000000000000000000002−2−22−222−2
χ362-2-22-2-222-2-22202-2-2000200-222-20000000000000000000000−222−22−2−22
χ3744-4-44-44-44i−4i4i−4i000000000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ30000000000000000000000
χ3844-4-44-44-44i−4i4i−4i00000000000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ30000000000000000000000
χ3944-4-44-44-4−4i4i−4i4i000000000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ0000000000000000000000
χ4044-4-44-44-4−4i4i−4i4i00000000000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ0000000000000000000000
χ414-44-44-4-440000400000-400000002i−2i2i−2i2i−2i2i−2i0000000000000000000000
χ424-44-44-4-440000400000-40000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000
χ434-44-44-4-440000-400000400000002-22-2-22-220000000000000000000000
χ444-44-44-4-440000-40000040000000-22-222-22-20000000000000000000000
χ454-44-4-444-44i−4i−4i4i000000000000000000000000000000002ζ3−2ζ32ζ−2ζ00000000
χ464-44-4-444-44i−4i−4i4i00000000000000000000000000000000−2ζ32ζ3−2ζ2ζ00000000
χ474-44-4-444-4−4i4i4i−4i000000000000000000000000000000002ζ−2ζ2ζ3−2ζ300000000
χ484-44-4-444-4−4i4i4i−4i00000000000000000000000000000000−2ζ2ζ−2ζ32ζ300000000
χ494-4-4444-4-4000000004i−4i000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ30000000000000000000000
χ504-4-4444-4-4000000004i−4i00000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ30000000000000000000000
χ514-4-4444-4-400000000−4i4i000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ0000000000000000000000
χ524-4-4444-4-400000000−4i4i00000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ0000000000000000000000
χ534-4-44-4-44444-4-40-44-40004000000000000000000000000000000000000
χ544-4-44-4-444-4-4440-444000-4000000000000000000000000000000000000
χ558888-8-8-8-8000000000000000000000000000000000000000000000000
χ5688-8-8-88-88000000000000000000000000000000000000000000000000

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