Finite Group Databasebeta

← Group #98744

Character table — Group #98744

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111111114444444444444488888888888816161616161616161616161616161616161616161616
order12222222224444444444442222444444444444448888888888888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-1-1-1-111-11111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111-1-1-1-111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ61111111111111111111111-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ71111111111111111111111-1-1-1-1-1-111-1-111-1-11-1-1111111111-1-1-1-1-1-1-1-1
χ81111111111111111111111-1-1-1-1-1-111-1-111-1-11-1-11-1-1-1-1-1-1-1-111111111
χ911111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ1111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111-1-11ii−i−i−i−iiiii−i−i−i−iii
χ1211111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111-1-11−i−iiiii−i−i−i−iiiii−i−i
χ1311111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111ii−i−i−i−iii−i−iiiii−i−i
χ1411111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111−i−iiiii−i−iii−i−i−i−iii
χ1511111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-111-1ii−i−iii−i−i−i−iii−i−iii
χ1611111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-111-1−i−iii−i−iiiii−i−iii−i−i
χ172222222222-2-2-2-22-222-2-22-222-2-2000000000002-200000000000000000
χ182222222222-2-2-2-22-222-2-22-2-2-22200000000000-2200000000000000000
χ192222222222-2-2-2-2-22-2-222-2222-2-200000000000-2200000000000000000
χ202222222222-2-2-2-2-22-2-222-22-2-222000000000002-200000000000000000
χ2122222222-2-222-2-222-2-2-2-2220000002200-2-200200-20000000000000000
χ2222222222-2-222-2-222-2-2-2-222000000-2-2002200-20020000000000000000
χ2322222222-2-222-2-2-2-22222-2-20000002200-2-200-20020000000000000000
χ2422222222-2-222-2-2-2-22222-2-2000000-2-2002200200-20000000000000000
χ2522222222-2-2-2-2222-2-2-2222-200002200-2-2002-200000000000000000000
χ2622222222-2-2-2-2222-2-2-2222-20000-2-2002200-2200000000000000000000
χ2722222222-2-2-2-222-2222-2-2-2200002200-2-200-2200000000000000000000
χ2822222222-2-2-2-222-2222-2-2-220000-2-20022002-200000000000000000000
χ294444-4-4-4-44-4000000000000004-4000000000000000000000000000000
χ304444-4-4-4-44-400000000000000-44000000000000000000000000000000
χ314444-4-4-4-4-440000000000004-400000000000000000000000000000000
χ324444-4-4-4-4-44000000000000-4400000000000000000000000000000000
χ3344-4-44-44-400000000004i−4i000000000000000000000000000000002ζ−2ζ2ζ3−2ζ3
χ3444-4-44-44-400000000004i−4i00000000000000000000000000000000−2ζ2ζ−2ζ32ζ3
χ3544-4-44-44-40000000000−4i4i000000000000000000000000000000002ζ3−2ζ32ζ−2ζ
χ3644-4-44-44-40000000000−4i4i00000000000000000000000000000000−2ζ32ζ3−2ζ2ζ
χ3744-4-4-44-440000000400000-400000000000000000000002i−2i2i−2i00000000
χ3844-4-4-44-440000000400000-40000000000000000000000−2i2i−2i2i00000000
χ3944-4-4-44-440000000-400000400000000000000000000002-2-2200000000
χ4044-4-4-44-440000000-40000040000000000000000000000-222-200000000
χ414-44-44-4-44000000400000-400000000000000000002i−2i2i−2i000000000000
χ424-44-44-4-44000000400000-40000000000000000000−2i2i−2i2i000000000000
χ434-44-44-4-44000000-400000400000000000000000002-2-22000000000000
χ444-44-44-4-44000000-40000040000000000000000000-222-2000000000000
χ454-44-4-444-4000000004i−4i0000000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ464-44-4-444-4000000004i−4i000000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ474-44-4-444-400000000−4i4i0000000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ484-44-4-444-400000000−4i4i000000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ494-4-4444-4-4004-4000000000000000000004i−4i0000000000000000000000
χ504-4-4444-4-4004-400000000000000000000−4i4i0000000000000000000000
χ514-4-4444-4-400-4400000000000000004i−4i00000000000000000000000000
χ524-4-4444-4-400-440000000000000000−4i4i00000000000000000000000000
χ534-4-44-4-44400004-400000000000000004-4000000000000000000000000
χ544-4-44-4-44400004-40000000000000000-44000000000000000000000000
χ554-4-44-4-4440000-440000000000004-40000000000000000000000000000
χ564-4-44-4-4440000-44000000000000-440000000000000000000000000000

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