Finite Group Databasebeta

← Group #116255

Character table — Group #116255

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order12222222222222224444224444444444444444444444444444442244444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1
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
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
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
χ911-1-111-1-111-1-111-1-111-1-11-111-1-1-11iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11-11-1i−ii−iii−i−i11-1-1
χ1011-1-111-1-111-1-111-1-111-1-11-111-1-1-11iiii−i−i−i−iiiii−i−i−i−i-1-1-1-111111-11-1−ii−ii−i−iii-1-111
χ1111-1-111-1-111-1-111-1-111-1-11-111-1-1-11iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-11-11i−ii−i−i−iii-1-111
χ1211-1-111-1-111-1-111-1-111-1-11-111-1-1-11iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111-11-11−ii−iiii−i−i11-1-1
χ1311-1-111-1-111-1-111-1-111-1-11-111-1-1-11−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-11-11−ii−iiii−i−i-1-111
χ1411-1-111-1-111-1-111-1-111-1-11-111-1-1-11−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111-11-11i−ii−i−i−iii11-1-1
χ1511-1-111-1-111-1-111-1-111-1-11-111-1-1-11−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11-11-1−ii−ii−i−iii11-1-1
χ1611-1-111-1-111-1-111-1-111-1-11-111-1-1-11−i−i−i−iiiii−i−i−i−iiiii-1-1-1-111111-11-1i−ii−iii−i−i-1-111
χ172222222222222222-2-2-2-222-2-2-2-2-2-222-2-222-2-200000000000000000000000000000000
χ182222222222222222-2-2-2-222-2-2-2-2-2-2-2-222-2-22200000000000000000000000000000000
χ192222222222-2-2-2-2222222-2-22-22-2-2-200000000000000000000000022-2-2000000000000
χ202222222222-2-2-2-2222222-2-22-22-2-2-2000000000000000000000000-2-222000000000000
χ212222222222-2-2-2-222-2-2-2-2-2-2-22-22220000000022-2-222-2-2000000000000000000000000
χ222222222222-2-2-2-222-2-2-2-2-2-2-22-222200000000-2-222-2-222000000000000000000000000
χ2322222222-2-22222-2-22222-2-2-22-22-2-2000000000000000000000000000022-2-200000000
χ2422222222-2-22222-2-22222-2-2-22-22-2-20000000000000000000000000000-2-22200000000
χ2522222222-2-22222-2-2-2-2-2-2-2-22-22-222000000000000000022-2-222-2-20000000000000000
χ2622222222-2-22222-2-2-2-2-2-2-2-22-22-2220000000000000000-2-222-2-2220000000000000000
χ2722222222-2-2-2-2-2-2-2-2222222-2-2-2-222000000000000000000000000000000002-22-20000
χ2822222222-2-2-2-2-2-2-2-2222222-2-2-2-22200000000000000000000000000000000-22-220000
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
χ3122-2-222-2-22222-2-2-2-222-2-2-222-2-222-20000000000000000000000002-2-22000000000000
χ3222-2-222-2-22222-2-2-2-222-2-2-222-2-222-2000000000000000000000000-222-2000000000000
χ3322-2-222-2-22222-2-2-2-2-2-222-22-222-2-22000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ3422-2-222-2-22222-2-2-2-2-2-222-22-222-2-2200000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ3522-2-222-2-222-2-222-2-2-2-2222-2-2-2222-22i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ3622-2-222-2-222-2-222-2-2-2-2222-2-2-2222-2−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ3722-2-222-2-2-2-222-2-22222-2-22-2-2-222-22000000000000000000000000000000002i−2i−2i2i0000
χ3822-2-222-2-2-2-222-2-22222-2-22-2-2-222-2200000000000000000000000000000000−2i2i2i−2i0000
χ3922-2-222-2-2-2-222-2-222-2-2222-222-2-22-20000000000000000000000000000000000002i−2i−2i2i
χ4022-2-222-2-2-2-222-2-222-2-2222-222-2-22-2000000000000000000000000000000000000−2i2i2i−2i
χ4122-2-222-2-2-2-2-2-2222222-2-2-22-222-22-200000000000000000000000000002i−2i−2i2i00000000
χ4222-2-222-2-2-2-2-2-2222222-2-2-22-222-22-20000000000000000000000000000−2i2i2i−2i00000000
χ4322-2-222-2-2-2-2-2-22222-2-222-222-2-22-22000000000000000022-2-2-2-2220000000000000000
χ4422-2-222-2-2-2-2-2-22222-2-222-222-2-22-220000000000000000-2-22222-2-20000000000000000
χ454444-4-4-4-44-400004-400000000000000000000000000002-22-22-22-20000000000000000
χ464444-4-4-4-44-400004-40000000000000000000000000000-22-22-22-220000000000000000
χ474444-4-4-4-4-440000-4400000000000000000000000000002-2-222-2-220000000000000000
χ484444-4-4-4-4-440000-440000000000000000000000000000-222-2-222-20000000000000000
χ4944-4-4-4-4444-40000-4400000000000000000000000000002-22-2-22-220000000000000000
χ5044-4-4-4-4444-40000-440000000000000000000000000000-22-222-22-20000000000000000
χ5144-4-4-4-444-4400004-400000000000000000000000000002-2-22-222-20000000000000000
χ5244-4-4-4-444-4400004-40000000000000000000000000000-222-22-2-220000000000000000
χ534-44-44-44-4000000004-44-4000000002i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000
χ544-44-44-44-4000000004-44-400000000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000
χ554-44-44-44-400000000-44-44000000002i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ564-44-44-44-400000000-44-4400000000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ574-44-4-44-44004-44-400000000000000000000002-22-22-22-2000000000000000000000000
χ584-44-4-44-44004-44-40000000000000000000000-22-22-22-22000000000000000000000000
χ594-44-4-44-4400-44-4400000000000000000000002-2-222-2-22000000000000000000000000
χ604-44-4-44-4400-44-440000000000000000000000-222-2-222-2000000000000000000000000
χ614-4-444-4-44000000004-4-44000000002-22-2-22-2200000000000000000000000000000000
χ624-4-444-4-44000000004-4-4400000000-22-222-22-200000000000000000000000000000000
χ634-4-444-4-4400000000-444-4000000002-2-22-222-200000000000000000000000000000000
χ644-4-444-4-4400000000-444-400000000-222-22-2-2200000000000000000000000000000000
χ654-4-44-444-4004-4-4400000000000000000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ664-4-44-444-4004-4-440000000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ674-4-44-444-400-444-400000000000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ684-4-44-444-400-444-40000000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000

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