Finite Group Databasebeta

← Group #238554

Character table — Group #238554

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111114444448888888888881616161616161616111111114444448888888888881616161616161616
order12222222444444888888888888224444442222222244444488888888888822444444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111-1-1-1-11-1-1-11-1-1-11111111111111111111111-1-1-1-11-1-1-11-1-1-1
χ3111111111111111111-1-1-1-11111-11-1-1-11-1-1111111111111111111-1-1-1-11111-11-1-1-11-1-1
χ4111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ511111111111111-1-1-1-111111111-1-111-1-1-1-111111111111111-1-1-1-111111111-1-111-1-1-1-1
χ611111111111111-1-1-1-11111-1-1-1-1-11-1-1-111111111111111111-1-1-1-11111-1-1-1-1-11-1-1-1111
χ711111111111111-1-1-1-1-1-1-1-111111-1-1-11-11111111111111111-1-1-1-1-1-1-1-111111-1-1-11-111
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
χ9222222222-2-22-2-2000000000000002-20000222222222-2-22-2-2000000000000002-20000
χ10222222222-2-22-2-200000000000000-220000222222222-2-22-2-200000000000000-220000
χ1122222222-22-2-22-200000000000002000-20022222222-22-2-22-200000000000002000-200
χ1222222222-22-2-22-20000000000000-200020022222222-22-2-22-20000000000000-2000200
χ1322222222-2-22-2-220000000000002000-200022222222-2-22-2-220000000000002000-2000
χ1422222222-2-22-2-22000000000000-2000200022222222-2-22-2-22000000000000-20002000
χ152-22-2-222-222-2-2-2200002i2i−2i−2i0000000000002-22-2-222-222-2-2-2200002i2i−2i−2i000000000000
χ162-22-2-222-222-2-2-220000−2i−2i2i2i0000000000002-22-2-222-222-2-2-220000−2i−2i2i2i000000000000
χ172-22-2-222-22-22-22-2000000002i2i−2i−2i000000002-22-2-222-22-22-22-2000000002i2i−2i−2i00000000
χ182-22-2-222-22-22-22-200000000−2i−2i2i2i000000002-22-2-222-22-22-22-200000000−2i−2i2i2i00000000
χ192-22-2-222-2-2222-2-20000000000000000002i−2i2-22-2-222-2-2222-2-20000000000000000002i−2i
χ202-22-2-222-2-2222-2-2000000000000000000−2i2i2-22-2-222-2-2222-2-2000000000000000000−2i2i
χ212-22-2-222-2-2-2-222222-2-200000000000000002-22-2-222-2-2-2-222222-2-20000000000000000
χ222-22-2-222-2-2-2-2222-2-22200000000000000002-22-2-222-2-2-2-2222-2-2220000000000000000
χ23444-4-4-4-440000002i−2i2i−2i0000000000000000444-4-4-4-440000002i−2i2i−2i0000000000000000
χ24444-4-4-4-44000000−2i2i−2i2i0000000000000000444-4-4-4-44000000−2i2i−2i2i0000000000000000
χ2544-44-44-4-400000000002i−2i2i−2i00000000000044-44-44-4-400000000002i−2i2i−2i000000000000
χ2644-44-44-4-40000000000−2i2i−2i2i00000000000044-44-44-4-40000000000−2i2i−2i2i000000000000
χ2744-4-44-44-4000000000000002i−2i2i−2i0000000044-4-44-44-4000000000000002i−2i2i−2i00000000
χ2844-4-44-44-400000000000000−2i2i−2i2i0000000044-4-44-44-400000000000000−2i2i−2i2i00000000
χ294-4444-4-4-40000002i−2i−2i2i00000000000000004-4444-4-4-40000002i−2i−2i2i0000000000000000
χ304-4444-4-4-4000000−2i2i2i−2i00000000000000004-4444-4-4-4000000−2i2i2i−2i0000000000000000
χ314-4-44-4-444000000000000002-2-22000000004-4-44-4-444000000000000002-2-2200000000
χ324-4-44-4-44400000000000000-222-2000000004-4-44-4-44400000000000000-222-200000000
χ334-4-4-444-4400000000002-2-220000000000004-4-4-444-4400000000002-2-22000000000000
χ344-4-4-444-440000000000-222-20000000000004-4-4-444-440000000000-222-2000000000000
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
χ361111111111111111111111-1-1-1-11-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1111-1111
χ37111111111111111111-1-1-1-11111-11-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1111-111
χ38111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1
χ3911111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111
χ4011111111111111-1-1-1-11111-1-1-1-1-11-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1111-1-1-1
χ4111111111111111-1-1-1-1-1-1-1-111111-1-1-11-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1111-11-1-1
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
χ43222222222-2-22-2-2000000000000002-20000-2-2-2-2-2-2-2-2-222-22200000000000000-220000
χ44222222222-2-22-2-200000000000000-220000-2-2-2-2-2-2-2-2-222-222000000000000002-20000
χ4522222222-22-2-22-200000000000002000-200-2-2-2-2-2-2-2-22-222-220000000000000-2000200
χ4622222222-22-2-22-20000000000000-2000200-2-2-2-2-2-2-2-22-222-2200000000000002000-200
χ4722222222-2-22-2-220000000000002000-2000-2-2-2-2-2-2-2-222-222-2000000000000-20002000
χ4822222222-2-22-2-22000000000000-20002000-2-2-2-2-2-2-2-222-222-20000000000002000-2000
χ492-22-2-222-222-2-2-2200002i2i−2i−2i000000000000-22-222-2-22-2-2222-20000−2i−2i2i2i000000000000
χ502-22-2-222-222-2-2-220000−2i−2i2i2i000000000000-22-222-2-22-2-2222-200002i2i−2i−2i000000000000
χ512-22-2-222-22-22-22-2000000002i2i−2i−2i00000000-22-222-2-22-22-22-2200000000−2i−2i2i2i00000000
χ522-22-2-222-22-22-22-200000000−2i−2i2i2i00000000-22-222-2-22-22-22-22000000002i2i−2i−2i00000000
χ532-22-2-222-2-2222-2-20000000000000000002i−2i-22-222-2-222-2-2-222000000000000000000−2i2i
χ542-22-2-222-2-2222-2-2000000000000000000−2i2i-22-222-2-222-2-2-2220000000000000000002i−2i
χ552-22-2-222-2-2-2-222222-2-20000000000000000-22-222-2-22222-2-2-2-2-2220000000000000000
χ562-22-2-222-2-2-2-2222-2-2220000000000000000-22-222-2-22222-2-2-222-2-20000000000000000
χ57444-4-4-4-440000002i−2i2i−2i0000000000000000-4-4-44444-4000000−2i2i−2i2i0000000000000000
χ58444-4-4-4-44000000−2i2i−2i2i0000000000000000-4-4-44444-40000002i−2i2i−2i0000000000000000
χ5944-44-44-4-400000000002i−2i2i−2i000000000000-4-44-44-4440000000000−2i2i−2i2i000000000000
χ6044-44-44-4-40000000000−2i2i−2i2i000000000000-4-44-44-44400000000002i−2i2i−2i000000000000
χ6144-4-44-44-4000000000000002i−2i2i−2i00000000-4-444-44-4400000000000000−2i2i−2i2i00000000
χ6244-4-44-44-400000000000000−2i2i−2i2i00000000-4-444-44-44000000000000002i−2i2i−2i00000000
χ634-4444-4-4-40000002i−2i−2i2i0000000000000000-44-4-4-4444000000−2i2i2i−2i0000000000000000
χ644-4444-4-4-4000000−2i2i2i−2i0000000000000000-44-4-4-44440000002i−2i−2i2i0000000000000000
χ654-4-44-4-444000000000000002-2-2200000000-444-444-4-400000000000000-222-200000000
χ664-4-44-4-44400000000000000-222-200000000-444-444-4-4000000000000002-2-2200000000
χ674-4-4-444-4400000000002-2-22000000000000-4444-4-44-40000000000-222-2000000000000
χ684-4-4-444-440000000000-222-2000000000000-4444-4-44-400000000002-2-22000000000000

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