Finite Group Databasebeta

← Group #239304

Character table — Group #239304

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122222244448888888888881616161616161616111122222244448888888888881616161616161616
order12222244442244444488888888244488882222224444224444448888888824448888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1
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
χ511111111111111-1-1-1-11111-1-1-1-11111-1-1-1-111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ711111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ811111111111111-1-1-1-1-1-1-1-11111-1-11111-1-111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ92222222222-2-2-2-2000022-2-20000000000002222222222-2-2-2-2000022-2-2000000000000
χ102222222222-2-2-2-20000-2-2220000000000002222222222-2-2-2-20000-2-222000000000000
χ11222222-2-2-2-222-2-2000000002i2i−2i−2i00000000222222-2-2-2-222-2-2000000002i2i−2i−2i00000000
χ12222222-2-2-2-222-2-200000000−2i−2i2i2i00000000222222-2-2-2-222-2-200000000−2i−2i2i2i00000000
χ13222222-2-2-2-2-2-22222-2-20000000000000000222222-2-2-2-2-2-22222-2-20000000000000000
χ14222222-2-2-2-2-2-222-2-2220000000000000000222222-2-2-2-2-2-222-2-2220000000000000000
χ152222-2-222-2-22-22-20000000000000000002i−2i2222-2-222-2-22-22-20000000000000000002i−2i
χ162222-2-222-2-22-22-2000000000000000000−2i2i2222-2-222-2-22-22-2000000000000000000−2i2i
χ172222-2-222-2-2-22-2200000000000000002i−2i002222-2-222-2-2-22-2200000000000000002i−2i00
χ182222-2-222-2-2-22-220000000000000000−2i2i002222-2-222-2-2-22-220000000000000000−2i2i00
χ192222-2-2-2-2222-2-220000000000002-20000002222-2-2-2-2222-2-220000000000002-2000000
χ202222-2-2-2-2222-2-22000000000000-220000002222-2-2-2-2222-2-22000000000000-22000000
χ212222-2-2-2-222-222-2000000000000002-200002222-2-2-2-222-222-2000000000000002-20000
χ222222-2-2-2-222-222-200000000000000-2200002222-2-2-2-222-222-200000000000000-220000
χ2344-4-4004i−4i0000002-22i−2i000000000000000044-4-4004i−4i0000002-22i−2i0000000000000000
χ2444-4-4004i−4i000000-22−2i2i000000000000000044-4-4004i−4i000000-22−2i2i0000000000000000
χ2544-4-400−4i4i0000002-2−2i2i000000000000000044-4-400−4i4i0000002-2−2i2i0000000000000000
χ2644-4-400−4i4i000000-222i−2i000000000000000044-4-400−4i4i000000-222i−2i0000000000000000
χ274-44-44-4000000000000002i2−2i20000000000004-44-44-4000000000000002i2−2i2000000000000
χ284-44-44-400000000000000−2i22i20000000000004-44-44-400000000000000−2i22i2000000000000
χ294-44-4-440000000000002i2−2i2000000000000004-44-4-440000000000002i2−2i200000000000000
χ304-44-4-44000000000000−2i22i2000000000000004-44-4-44000000000000−2i22i200000000000000
χ314-4-4400004-40000000000002i−2i2i−2i000000004-4-4400004-40000000000002i−2i2i−2i00000000
χ324-4-4400004-4000000000000−2i2i−2i2i000000004-4-4400004-4000000000000−2i2i−2i2i00000000
χ334-4-440000-440000000000002-2-22000000004-4-440000-440000000000002-2-2200000000
χ344-4-440000-44000000000000-222-2000000004-4-440000-44000000000000-222-200000000
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
χ3611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ37111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111
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
χ3911111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ4011111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ4111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ4211111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ432222222222-2-2-2-2000022-2-2000000000000-2-2-2-2-2-2-2-2-2-222220000-2-222000000000000
χ442222222222-2-2-2-20000-2-222000000000000-2-2-2-2-2-2-2-2-2-22222000022-2-2000000000000
χ45222222-2-2-2-222-2-2000000002i2i−2i−2i00000000-2-2-2-2-2-22222-2-22200000000−2i−2i2i2i00000000
χ46222222-2-2-2-222-2-200000000−2i−2i2i2i00000000-2-2-2-2-2-22222-2-222000000002i2i−2i−2i00000000
χ47222222-2-2-2-2-2-22222-2-20000000000000000-2-2-2-2-2-2222222-2-2-2-2220000000000000000
χ48222222-2-2-2-2-2-222-2-2220000000000000000-2-2-2-2-2-2222222-2-222-2-20000000000000000
χ492222-2-222-2-22-22-20000000000000000002i−2i-2-2-2-222-2-222-22-22000000000000000000−2i2i
χ502222-2-222-2-22-22-2000000000000000000−2i2i-2-2-2-222-2-222-22-220000000000000000002i−2i
χ512222-2-222-2-2-22-2200000000000000002i−2i00-2-2-2-222-2-2222-22-20000000000000000−2i2i00
χ522222-2-222-2-2-22-220000000000000000−2i2i00-2-2-2-222-2-2222-22-200000000000000002i−2i00
χ532222-2-2-2-2222-2-220000000000002-2000000-2-2-2-22222-2-2-222-2000000000000-22000000
χ542222-2-2-2-2222-2-22000000000000-22000000-2-2-2-22222-2-2-222-20000000000002-2000000
χ552222-2-2-2-222-222-2000000000000002-20000-2-2-2-22222-2-22-2-2200000000000000-220000
χ562222-2-2-2-222-222-200000000000000-220000-2-2-2-22222-2-22-2-22000000000000002-20000
χ5744-4-4004i−4i0000002-22i−2i0000000000000000-4-44400−4i4i000000-22−2i2i0000000000000000
χ5844-4-4004i−4i000000-22−2i2i0000000000000000-4-44400−4i4i0000002-22i−2i0000000000000000
χ5944-4-400−4i4i0000002-2−2i2i0000000000000000-4-444004i−4i000000-222i−2i0000000000000000
χ6044-4-400−4i4i000000-222i−2i0000000000000000-4-444004i−4i0000002-2−2i2i0000000000000000
χ614-44-44-4000000000000002i2−2i2000000000000-44-44-4400000000000000−2i22i2000000000000
χ624-44-44-400000000000000−2i22i2000000000000-44-44-44000000000000002i2−2i2000000000000
χ634-44-4-440000000000002i2−2i200000000000000-44-444-4000000000000−2i22i200000000000000
χ644-44-4-44000000000000−2i22i200000000000000-44-444-40000000000002i2−2i200000000000000
χ654-4-4400004-40000000000002i−2i2i−2i00000000-444-40000-44000000000000−2i2i−2i2i00000000
χ664-4-4400004-4000000000000−2i2i−2i2i00000000-444-40000-440000000000002i−2i2i−2i00000000
χ674-4-440000-440000000000002-2-2200000000-444-400004-4000000000000-222-200000000
χ684-4-440000-44000000000000-222-200000000-444-400004-40000000000002-2-2200000000

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