Finite Group Databasebeta

← Group #236708

Character table — Group #236708

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111222244444888888881616161616161616161611112222444448888888816161616161616161616
order12222244444448888888822444488882222224444444888888882244448888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111-1-1-1-1-1-111-1-1111111111111111111111-1-1-1-1-1-111-1-1
χ311111111111111111-1-1-1-11-1111-1-1-1-1-111111111111111111-1-1-1-11-1111-1-1-1-1-1
χ411111111111111111-1-1-1-1-11-1-1-11-1-11111111111111111111-1-1-1-1-11-1-1-11-1-111
χ51111111111111-1-1-1-111111-11-1-1-1-1-1111111111111111-1-1-1-111111-11-1-1-1-1-111
χ61111111111111-1-1-1-11111-11-1111-1-1-1-11111111111111-1-1-1-11111-11-1111-1-1-1-1
χ71111111111111-1-1-1-1-1-1-1-1111-1-1111-1-11111111111111-1-1-1-1-1-1-1-1111-1-1111-1-1
χ81111111111111-1-1-1-1-1-1-1-1-1-1-111-111111111111111111-1-1-1-1-1-1-1-1-1-1-111-11111
χ922222222-2-2-2-220000000002000-2000022222222-2-2-2-220000000002000-20000
χ1022222222-2-2-2-22000000000-20002000022222222-2-2-2-22000000000-200020000
χ11222222-2-222-2-2-200000000000000002i−2i222222-2-222-2-2-200000000000000002i−2i
χ12222222-2-222-2-2-20000000000000000−2i2i222222-2-222-2-2-20000000000000000−2i2i
χ13222222-2-2-2-222-222-2-200000000000000222222-2-2-2-222-222-2-200000000000000
χ14222222-2-2-2-222-2-2-22200000000000000222222-2-2-2-222-2-2-22200000000000000
χ152222-2-2222-22-2-20000000020-200000002222-2-2222-22-2-20000000020-20000000
χ162222-2-2222-22-2-200000000-20200000002222-2-2222-22-2-200000000-2020000000
χ172222-2-222-22-22-2000000000000002-2002222-2-222-22-22-2000000000000002-200
χ182222-2-222-22-22-200000000000000-22002222-2-222-22-22-200000000000000-2200
χ192222-2-2-2-22-2-222000022-2-200000000002222-2-2-2-22-2-222000022-2-20000000000
χ202222-2-2-2-22-2-2220000-2-22200000000002222-2-2-2-22-2-2220000-2-2220000000000
χ212222-2-2-2-2-222-22000000000002-2000002222-2-2-2-2-222-22000000000002-200000
χ222222-2-2-2-2-222-2200000000000-22000002222-2-2-2-2-222-2200000000000-2200000
χ234-44-44-40000000002i2−2i2000000000000004-44-44-40000000002i2−2i200000000000000
χ244-44-44-4000000000−2i22i2000000000000004-44-44-4000000000−2i22i200000000000000
χ254-44-4-4400000002i2−2i200000000000000004-44-4-4400000002i2−2i20000000000000000
χ264-44-4-440000000−2i22i200000000000000004-44-4-440000000−2i22i20000000000000000
χ274-4-44004-40000000002-22-200000000004-4-44004-40000000002-22-20000000000
χ284-4-44004-4000000000-22-2200000000004-4-44004-4000000000-22-220000000000
χ294-4-4400-440000000002-2-2200000000004-4-4400-440000000002-2-220000000000
χ304-4-4400-44000000000-222-200000000004-4-4400-44000000000-222-20000000000
χ3188-8-800000000000000000000000000088-8-8000000000000000000000000000
χ321111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ33111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111
χ3411111111111111111-1-1-1-11-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-1-111111
χ3511111111111111111-1-1-1-1-11-1-1-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1111-111-1-1
χ361111111111111-1-1-1-111111-11-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11-111111-1-1
χ371111111111111-1-1-1-11111-11-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-11-1-1-11111
χ381111111111111-1-1-1-1-1-1-1-1111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-111-1-1-111
χ391111111111111-1-1-1-1-1-1-1-1-1-1-111-11111-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-11-1-1-1-1
χ4022222222-2-2-2-220000000002000-20000-2-2-2-2-2-2-2-22222-2000000000-200020000
χ4122222222-2-2-2-22000000000-200020000-2-2-2-2-2-2-2-22222-20000000002000-20000
χ42222222-2-222-2-2-200000000000000002i−2i-2-2-2-2-2-222-2-22220000000000000000−2i2i
χ43222222-2-222-2-2-20000000000000000−2i2i-2-2-2-2-2-222-2-222200000000000000002i−2i
χ44222222-2-2-2-222-222-2-200000000000000-2-2-2-2-2-22222-2-22-2-22200000000000000
χ45222222-2-2-2-222-2-2-22200000000000000-2-2-2-2-2-22222-2-2222-2-200000000000000
χ462222-2-2222-22-2-20000000020-20000000-2-2-2-222-2-2-22-22200000000-2020000000
χ472222-2-2222-22-2-200000000-2020000000-2-2-2-222-2-2-22-2220000000020-20000000
χ482222-2-222-22-22-2000000000000002-200-2-2-2-222-2-22-22-2200000000000000-2200
χ492222-2-222-22-22-200000000000000-2200-2-2-2-222-2-22-22-22000000000000002-200
χ502222-2-2-2-22-2-222000022-2-20000000000-2-2-2-22222-222-2-20000-2-2220000000000
χ512222-2-2-2-22-2-2220000-2-2220000000000-2-2-2-22222-222-2-2000022-2-20000000000
χ522222-2-2-2-2-222-22000000000002-200000-2-2-2-222222-2-22-200000000000-2200000
χ532222-2-2-2-2-222-2200000000000-2200000-2-2-2-222222-2-22-2000000000002-200000
χ544-44-44-40000000002i2−2i200000000000000-44-44-44000000000−2i22i200000000000000
χ554-44-44-4000000000−2i22i200000000000000-44-44-440000000002i2−2i200000000000000
χ564-44-4-4400000002i2−2i20000000000000000-44-444-40000000−2i22i20000000000000000
χ574-44-4-440000000−2i22i20000000000000000-44-444-400000002i2−2i20000000000000000
χ584-4-44004-40000000002-22-20000000000-444-400-44000000000-22-220000000000
χ594-4-44004-4000000000-22-220000000000-444-400-440000000002-22-20000000000
χ604-4-4400-440000000002-2-220000000000-444-4004-4000000000-222-20000000000
χ614-4-4400-44000000000-222-20000000000-444-4004-40000000002-2-220000000000
χ6288-8-8000000000000000000000000000-8-888000000000000000000000000000

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