Finite Group Databasebeta

← Group #234352

Character table — Group #234352

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122222244448888888888881616161616161616111122222244448888888888881616161616161616
order12222222442444444444444444224488882222222244244444444444444422448888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111-1-1-1-11-11-1-1-1-1-11111111111111111111111-1-1-1-11-11-1-1-1-1-1
χ3111111111111111111-1-1-1-11111-11-11-1-1-1-1111111111111111111-1-1-1-11111-11-11-1-1-1-1
χ4111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111-1-1-1-111111111-1-1-1-111-1-111111111111111-1-1-1-111111111-1-1-1-111-1-1
χ611111111111111-1-1-1-11111-1-1-1-1-11-11-1-11111111111111111-1-1-1-11111-1-1-1-1-11-11-1-111
χ711111111111111-1-1-1-1-1-1-1-111111-11-1-1-11111111111111111-1-1-1-1-1-1-1-111111-11-1-1-111
χ811111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ922222222-2-22-2-2-222-2-2000000000000000022222222-2-22-2-2-222-2-20000000000000000
χ1022222222-2-22-2-2-2-2-222000000000000000022222222-2-22-2-2-2-2-2220000000000000000
χ11222222-2-222-22-2-200000000000020-200000222222-2-222-22-2-200000000000020-200000
χ12222222-2-222-22-2-2000000000000-20200000222222-2-222-22-2-2000000000000-20200000
χ13222222-2-2-2-2-2-222000022-2-2000000000000222222-2-2-2-2-2-222000022-2-2000000000000
χ14222222-2-2-2-2-2-2220000-2-222000000000000222222-2-2-2-2-2-2220000-2-222000000000000
χ152222-2-22222-2-22-2000000000000020-200002222-2-22222-2-22-2000000000000020-20000
χ162222-2-22222-2-22-20000000000000-20200002222-2-22222-2-22-20000000000000-2020000
χ172222-2-222-2-2-22-220000000022-2-2000000002222-2-222-2-2-22-220000000022-2-200000000
χ182222-2-222-2-2-22-2200000000-2-222000000002222-2-222-2-2-22-2200000000-2-22200000000
χ192222-2-2-2-2222-2-2200000000000000002-2002222-2-2-2-2222-2-2200000000000000002-200
χ202222-2-2-2-2222-2-220000000000000000-22002222-2-2-2-2222-2-220000000000000000-2200
χ212222-2-2-2-2-2-2222-20000000000000000002i−2i2222-2-2-2-2-2-2222-20000000000000000002i−2i
χ222222-2-2-2-2-2-2222-2000000000000000000−2i2i2222-2-2-2-2-2-2222-2000000000000000000−2i2i
χ2344-4-4004-400000000002i−2i2i−2i00000000000044-4-4004-400000000002i−2i2i−2i000000000000
χ2444-4-4004-40000000000−2i2i−2i2i00000000000044-4-4004-40000000000−2i2i−2i2i000000000000
χ2544-4-400-4400000000002i−2i−2i2i00000000000044-4-400-4400000000002i−2i−2i2i000000000000
χ2644-4-400-440000000000−2i2i2i−2i00000000000044-4-400-440000000000−2i2i2i−2i000000000000
χ274-44-44-400000000000000002i−2i2i−2i000000004-44-44-400000000000000002i−2i2i−2i00000000
χ284-44-44-40000000000000000−2i2i−2i2i000000004-44-44-40000000000000000−2i2i−2i2i00000000
χ294-44-4-4400000000000000002i−2i−2i2i000000004-44-4-4400000000000000002i−2i−2i2i00000000
χ304-44-4-440000000000000000−2i2i2i−2i000000004-44-4-440000000000000000−2i2i2i−2i00000000
χ314-4-4400004-400002-22-200000000000000004-4-4400004-400002-22-20000000000000000
χ324-4-4400004-40000-22-2200000000000000004-4-4400004-40000-22-220000000000000000
χ334-4-440000-4400002-2-2200000000000000004-4-440000-4400002-2-220000000000000000
χ344-4-440000-440000-222-200000000000000004-4-440000-440000-222-20000000000000000
χ351111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ361111111111111111111111-1-1-1-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-111111
χ37111111111111111111-1-1-1-11111-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-11-11111
χ38111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ3911111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ4011111111111111-1-1-1-11111-1-1-1-1-11-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-11-111-1-1
χ4111111111111111-1-1-1-1-1-1-1-111111-11-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1111-1-1
χ4211111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ4322222222-2-22-2-2-222-2-20000000000000000-2-2-2-2-2-2-2-222-2222-2-2220000000000000000
χ4422222222-2-22-2-2-2-2-2220000000000000000-2-2-2-2-2-2-2-222-222222-2-20000000000000000
χ45222222-2-222-22-2-200000000000020-200000-2-2-2-2-2-222-2-22-222000000000000-20200000
χ46222222-2-222-22-2-2000000000000-20200000-2-2-2-2-2-222-2-22-22200000000000020-200000
χ47222222-2-2-2-2-2-222000022-2-2000000000000-2-2-2-2-2-2222222-2-20000-2-222000000000000
χ48222222-2-2-2-2-2-2220000-2-222000000000000-2-2-2-2-2-2222222-2-2000022-2-2000000000000
χ492222-2-22222-2-22-2000000000000020-20000-2-2-2-222-2-2-2-222-220000000000000-2020000
χ502222-2-22222-2-22-20000000000000-2020000-2-2-2-222-2-2-2-222-22000000000000020-20000
χ512222-2-222-2-2-22-220000000022-2-200000000-2-2-2-222-2-2222-22-200000000-2-22200000000
χ522222-2-222-2-2-22-2200000000-2-22200000000-2-2-2-222-2-2222-22-20000000022-2-200000000
χ532222-2-2-2-2222-2-2200000000000000002-200-2-2-2-22222-2-2-222-20000000000000000-2200
χ542222-2-2-2-2222-2-220000000000000000-2200-2-2-2-22222-2-2-222-200000000000000002-200
χ552222-2-2-2-2-2-2222-20000000000000000002i−2i-2-2-2-2222222-2-2-22000000000000000000−2i2i
χ562222-2-2-2-2-2-2222-2000000000000000000−2i2i-2-2-2-2222222-2-2-220000000000000000002i−2i
χ5744-4-4004-400000000002i−2i2i−2i000000000000-4-44400-440000000000−2i2i−2i2i000000000000
χ5844-4-4004-40000000000−2i2i−2i2i000000000000-4-44400-4400000000002i−2i2i−2i000000000000
χ5944-4-400-4400000000002i−2i−2i2i000000000000-4-444004-40000000000−2i2i2i−2i000000000000
χ6044-4-400-440000000000−2i2i2i−2i000000000000-4-444004-400000000002i−2i−2i2i000000000000
χ614-44-44-400000000000000002i−2i2i−2i00000000-44-44-440000000000000000−2i2i−2i2i00000000
χ624-44-44-40000000000000000−2i2i−2i2i00000000-44-44-4400000000000000002i−2i2i−2i00000000
χ634-44-4-4400000000000000002i−2i−2i2i00000000-44-444-40000000000000000−2i2i2i−2i00000000
χ644-44-4-440000000000000000−2i2i2i−2i00000000-44-444-400000000000000002i−2i−2i2i00000000
χ654-4-4400004-400002-22-20000000000000000-444-40000-440000-22-220000000000000000
χ664-4-4400004-40000-22-220000000000000000-444-40000-4400002-22-20000000000000000
χ674-4-440000-4400002-2-220000000000000000-444-400004-40000-222-20000000000000000
χ684-4-440000-440000-222-20000000000000000-444-400004-400002-2-220000000000000000

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