Finite Group Databasebeta

← Group #116352

Character table — Group #116352

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order12222222222222222222222222224444444444444444444444444444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911-111-1-1-11111-1-111-1-1-1-1111-1-1-1-111111-1-1-1-1ii−i−iii−i−iii−i−iii−i−iii−i−iii−i−i11-1-111-1-1
χ1011-111-1-1-11111-1-111-1-1-1-1111-1-1-1-111111-1-1-1-1ii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii-1-111-1-111
χ1111-111-1-1-11111-1-111-1-1-1-1111-1-1-1-111111-1-1-1-1−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i-1-111-1-111
χ1211-111-1-1-11111-1-111-1-1-1-1111-1-1-1-111111-1-1-1-1−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii11-1-111-1-1
χ1311-111-1-1-11111-1-111-1-1-1-1111-1-1-1-11-1-1-1-11111ii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii11-1-1-1-111
χ1411-111-1-1-11111-1-111-1-1-1-1111-1-1-1-11-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i-1-11111-1-1
χ1511-111-1-1-11111-1-111-1-1-1-1111-1-1-1-11-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iii-1-11111-1-1
χ1611-111-1-1-11111-1-111-1-1-1-1111-1-1-1-11-1-1-1-11111−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−i11-1-1-1-111
χ17222222222222-2-2-2-222222-2-22-2-2-2-222-2-222-2-200000000000000000000000000000000
χ18222222222222-2-2-2-222222-2-22-2-2-2-2-2-222-2-22200000000000000000000000000000000
χ192222222222-2-2222222-2-2-22-2-22-2-2-200000000000022220000-2-2-2-20000000000000000
χ202222222222-2-2222222-2-2-22-2-22-2-2-2000000000000-2-2-2-2000022220000000000000000
χ212222222222-2-2-2-2-2-222-2-2-2-22-2-222200000000000000000000000000002-22-200000000
χ222222222222-2-2-2-2-2-222-2-2-2-22-2-22220000000000000000000000000000-22-2200000000
χ2322222222-2-2222222-2-222-2-22-2-22-2-20000000022220000-2-2-2-200000000000000000000
χ2422222222-2-2222222-2-222-2-22-2-22-2-200000000-2-2-2-20000222200000000000000000000
χ2522222222-2-222-2-2-2-2-2-222-22-2-22-2220000000000000000000000002-22-2000000000000
χ2622222222-2-222-2-2-2-2-2-222-22-2-22-222000000000000000000000000-22-22000000000000
χ2722222222-2-2-2-22222-2-2-2-22-2-22-2-222000000000000000000000000000000002-22-20000
χ2822222222-2-2-2-22222-2-2-2-22-2-22-2-22200000000000000000000000000000000-22-220000
χ2922222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-20000000000000000000000000000000000002i−2i2i−2i
χ3022222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2000000000000000000000000000000000000−2i2i−2i2i
χ3122-222-2-2-2222222-2-2-2-2-2-22-2-2-2222-222-2-2-2-22200000000000000000000000000000000
χ3222-222-2-2-2222222-2-2-2-2-2-22-2-2-2222-2-2-22222-2-200000000000000000000000000000000
χ3322-222-2-2-222-2-222-2-2-2-222-2-2222-2-2200000000000000000000000000002i−2i−2i2i00000000
χ3422-222-2-2-222-2-222-2-2-2-222-2-2222-2-220000000000000000000000000000−2i2i2i−2i00000000
χ3522-222-2-2-222-2-2-2-222-2-222-22-22-222-20000000000002i2i−2i−2i0000−2i−2i2i2i0000000000000000
χ3622-222-2-2-222-2-2-2-222-2-222-22-22-222-2000000000000−2i−2i2i2i00002i2i−2i−2i0000000000000000
χ3722-222-2-2-2-2-22222-2-222-2-2-22-22-22-220000000000000000000000002i−2i−2i2i000000000000
χ3822-222-2-2-2-2-22222-2-222-2-2-22-22-22-22000000000000000000000000−2i2i2i−2i000000000000
χ3922-222-2-2-2-2-222-2-22222-2-2-2-2222-22-2000000002i2i−2i−2i0000−2i−2i2i2i00000000000000000000
χ4022-222-2-2-2-2-222-2-22222-2-2-2-2222-22-200000000−2i−2i2i2i00002i2i−2i−2i00000000000000000000
χ4122-222-2-2-2-2-2-2-222-2-22222222-2-2-22-20000000000000000000000000000000000002i−2i−2i2i
χ4222-222-2-2-2-2-2-2-222-2-22222222-2-2-22-2000000000000000000000000000000000000−2i2i2i−2i
χ4322-222-2-2-2-2-2-2-2-2-22222222-2-2-222-22000000000000000000000000000000002-2-220000
χ4422-222-2-2-2-2-2-2-2-2-22222222-2-2-222-2200000000000000000000000000000000-222-20000
χ45444-4-4-4-4400004-44-40000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000
χ46444-4-4-4-4400004-44-4000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000
χ47444-4-4-4-440000-44-440000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ48444-4-4-4-440000-44-44000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ4944-4-4-444-400004-4-440000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ5044-4-4-444-400004-4-44000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ5144-4-4-444-40000-444-40000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ5244-4-4-444-40000-444-4000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ534-444-44-4-4004-40000004-4000000000000000000002i−2i2i−2i00002i−2i2i−2i0000000000000000
χ544-444-44-4-4004-40000004-400000000000000000000−2i2i−2i2i0000−2i2i−2i2i0000000000000000
χ554-444-44-4-400-44000000-44000000000000000000002i−2i2i−2i0000−2i2i−2i2i0000000000000000
χ564-444-44-4-400-44000000-4400000000000000000000−2i2i−2i2i00002i−2i2i−2i0000000000000000
χ574-44-44-44-44-40000004-40000000000000000002i−2i2i−2i00002i−2i2i−2i00000000000000000000
χ584-44-44-44-44-40000004-4000000000000000000−2i2i−2i2i0000−2i2i−2i2i00000000000000000000
χ594-44-44-44-4-44000000-440000000000000000002i−2i2i−2i0000−2i2i−2i2i00000000000000000000
χ604-44-44-44-4-44000000-44000000000000000000−2i2i−2i2i00002i−2i2i−2i00000000000000000000
χ614-4-44-4-444004-4000000-44000000000000000000002-2-2200002-2-220000000000000000
χ624-4-44-4-444004-4000000-4400000000000000000000-222-20000-222-20000000000000000
χ634-4-44-4-44400-440000004-4000000000000000000002-2-220000-222-20000000000000000
χ644-4-44-4-44400-440000004-400000000000000000000-222-200002-2-220000000000000000
χ654-4-4-444-444-4000000-440000000000000000002-2-2200002-2-2200000000000000000000
χ664-4-4-444-444-4000000-44000000000000000000-222-20000-222-200000000000000000000
χ674-4-4-444-44-440000004-40000000000000000002-2-220000-222-200000000000000000000
χ684-4-4-444-44-440000004-4000000000000000000-222-200002-2-2200000000000000000000

Here i is the imaginary unit (i² = −1).