Finite Group Databasebeta

← Group #233321

Character table — Group #233321

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112222224444444444441616161616161616161616161111222222444444444444161616161616161616161616
order12224444442444444444444444448888882222444444244444444444444444888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111-1-1-1-111-1-1-1-1111111111111111111111111-1-1-1-111-1-1-1-1
χ31111111111111111111111-1-111-1-1-1-111-1-11111111111111111111111-1-111-1-1-1-111-1-1
χ41111111111111111111111-1-1-1-111-1-1-1-1111111111111111111111111-1-1-1-111-1-1-1-111
χ511111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ611111111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111111111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ711111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ811111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ9222222-222-2-22-2-20000000000002-2000000222222-222-2-22-2-20000000000002-2000000
χ10222222-222-2-22-2-2000000000000-22000000222222-222-2-22-2-2000000000000-22000000
χ1122222-222-22-2-22-200000000002-20000000022222-222-22-2-22-200000000002-200000000
χ1222222-222-22-2-22-20000000000-220000000022222-222-22-2-22-20000000000-2200000000
χ1322222-2-22-2-22-2-22000000000000002-2000022222-2-22-2-22-2-22000000000000002-20000
χ1422222-2-22-2-22-2-2200000000000000-22000022222-2-22-2-22-2-2200000000000000-220000
χ152222-222-222-2-2-22000000002-200000000002222-222-222-2-2-22000000002-20000000000
χ162222-222-222-2-2-2200000000-2200000000002222-222-222-2-2-2200000000-220000000000
χ172222-22-2-22-22-22-200000000000000002-2002222-22-2-22-22-22-200000000000000002-200
χ182222-22-2-22-22-22-20000000000000000-22002222-22-2-22-22-22-20000000000000000-2200
χ192222-2-22-2-2222-2-20000000000000000002-22222-2-22-2-2222-2-20000000000000000002-2
χ202222-2-22-2-2222-2-2000000000000000000-222222-2-22-2-2222-2-2000000000000000000-22
χ212222-2-2-2-2-2-2-22222i2i2i2i−2i−2i−2i−2i0000000000002222-2-2-2-2-2-2-22222i2i2i2i−2i−2i−2i−2i000000000000
χ222222-2-2-2-2-2-2-2222−2i−2i−2i−2i2i2i2i2i0000000000002222-2-2-2-2-2-2-2222−2i−2i−2i−2i2i2i2i2i000000000000
χ2344-4-400400-4000022-2-222-2-200000000000044-4-400400-4000022-2-222-2-2000000000000
χ2444-4-400400-40000-2-222-2-22200000000000044-4-400400-40000-2-222-2-222000000000000
χ2544-4-400-400400002i2i−2i−2i−2i−2i2i2i00000000000044-4-400-400400002i2i−2i−2i−2i−2i2i2i000000000000
χ2644-4-400-40040000−2i−2i2i2i2i2i−2i−2i00000000000044-4-400-40040000−2i−2i2i2i2i2i−2i−2i000000000000
χ274-44-40400-4000002-22-22-22-20000000000004-44-40400-4000002-22-22-22-2000000000000
χ284-44-40400-400000-22-22-22-220000000000004-44-40400-400000-22-22-22-22000000000000
χ294-44-40-4004000002i−2i2i−2i−2i2i−2i2i0000000000004-44-40-4004000002i−2i2i−2i−2i2i−2i2i000000000000
χ304-44-40-400400000−2i2i−2i2i2i−2i2i−2i0000000000004-44-40-400400000−2i2i−2i2i2i−2i2i−2i000000000000
χ314-4-44400-40000002-2-222-2-220000000000004-4-44400-40000002-2-222-2-22000000000000
χ324-4-44400-4000000-222-2-222-20000000000004-4-44400-4000000-222-2-222-2000000000000
χ334-4-44-40040000002i−2i−2i2i−2i2i2i−2i0000000000004-4-44-40040000002i−2i−2i2i−2i2i2i−2i000000000000
χ344-4-44-4004000000−2i2i2i−2i2i−2i−2i2i0000000000004-4-44-4004000000−2i2i2i−2i2i−2i−2i2i000000000000
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
χ36111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ371111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111
χ381111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1
χ3911111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ4011111111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-111
χ4111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111
χ4211111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1
χ43222222-222-2-22-2-20000000000002-2000000-2-2-2-2-2-22-2-222-222000000000000-22000000
χ44222222-222-2-22-2-2000000000000-22000000-2-2-2-2-2-22-2-222-2220000000000002-2000000
χ4522222-222-22-2-22-200000000002-200000000-2-2-2-2-22-2-22-222-220000000000-2200000000
χ4622222-222-22-2-22-20000000000-2200000000-2-2-2-2-22-2-22-222-2200000000002-200000000
χ4722222-2-22-2-22-2-22000000000000002-20000-2-2-2-2-222-222-222-200000000000000-220000
χ4822222-2-22-2-22-2-2200000000000000-220000-2-2-2-2-222-222-222-2000000000000002-20000
χ492222-222-222-2-2-22000000002-20000000000-2-2-2-22-2-22-2-2222-200000000-220000000000
χ502222-222-222-2-2-2200000000-220000000000-2-2-2-22-2-22-2-2222-2000000002-20000000000
χ512222-22-2-22-22-22-200000000000000002-200-2-2-2-22-222-22-22-220000000000000000-2200
χ522222-22-2-22-22-22-20000000000000000-2200-2-2-2-22-222-22-22-2200000000000000002-200
χ532222-2-22-2-2222-2-20000000000000000002-2-2-2-2-222-222-2-2-222000000000000000000-22
χ542222-2-22-2-2222-2-2000000000000000000-22-2-2-2-222-222-2-2-2220000000000000000002-2
χ552222-2-2-2-2-2-2-22222i2i2i2i−2i−2i−2i−2i000000000000-2-2-2-22222222-2-2-2−2i−2i−2i−2i2i2i2i2i000000000000
χ562222-2-2-2-2-2-2-2222−2i−2i−2i−2i2i2i2i2i000000000000-2-2-2-22222222-2-2-22i2i2i2i−2i−2i−2i−2i000000000000
χ5744-4-400400-4000022-2-222-2-2000000000000-4-44400-40040000-2-222-2-222000000000000
χ5844-4-400400-40000-2-222-2-222000000000000-4-44400-4004000022-2-222-2-2000000000000
χ5944-4-400-400400002i2i−2i−2i−2i−2i2i2i000000000000-4-44400400-40000−2i−2i2i2i2i2i−2i−2i000000000000
χ6044-4-400-40040000−2i−2i2i2i2i2i−2i−2i000000000000-4-44400400-400002i2i−2i−2i−2i−2i2i2i000000000000
χ614-44-40400-4000002-22-22-22-2000000000000-44-440-400400000-22-22-22-22000000000000
χ624-44-40400-400000-22-22-22-22000000000000-44-440-4004000002-22-22-22-2000000000000
χ634-44-40-4004000002i−2i2i−2i−2i2i−2i2i000000000000-44-440400-400000−2i2i−2i2i2i−2i2i−2i000000000000
χ644-44-40-400400000−2i2i−2i2i2i−2i2i−2i000000000000-44-440400-4000002i−2i2i−2i−2i2i−2i2i000000000000
χ654-4-44400-40000002-2-222-2-22000000000000-444-4-4004000000-222-2-222-2000000000000
χ664-4-44400-4000000-222-2-222-2000000000000-444-4-40040000002-2-222-2-22000000000000
χ674-4-44-40040000002i−2i−2i2i−2i2i2i−2i000000000000-444-4400-4000000−2i2i2i−2i2i−2i−2i2i000000000000
χ684-4-44-4004000000−2i2i2i−2i2i−2i−2i2i000000000000-444-4400-40000002i−2i−2i2i−2i2i2i−2i000000000000

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