Finite Group Databasebeta

← Group #338359

Character table — Group #338359

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11111111222222224444448888888888888888888888161616161616161616161616323232
order12222222444444444488882244444488888888888888444444888888244
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-11-111-1-1-1-1-1-1-1-111-1
χ3111111111111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-111-1-1-1-11
χ4111111111111111111111111-1-1-1-1-1-111-1-1-1-1111111111-111-1-111-1-111-1-1-1
χ51111111111111111111111-1-111111111111111111111-11-1-1-1-1-1-111-1-1-1-1-1
χ61111111111111111111111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-11
χ71111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-11-1-1-1-111111111-1
χ81111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1111
χ9111111111111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-11-1-1
χ10111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-111111-11
χ11111111111111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1111111-1-111-1-1-1-111-11-1
χ12111111111111111111-1-1-1-111-1-1-1-1-1-1111111-1-111-1-1-1-11-1-1-1-1-11111-1-1-111
χ13111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1111-1-1-1-1-1-111-111
χ14111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-11-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1111-1-111-1-1-1-11-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-111111-1-1
χ17222222222-22-22-22-2-2-200000022-2-222-2-20000002200000-20000000000000
χ18222222222-22-22-22-2-2-200000022-2-2-2-222000000-2-20000020000000000000
χ19222222222-22-22-22-2-2-2000000-2-2222222000000-2-200000-20000000000000
χ20222222222-22-22-22-2-2-2000000-2-222-2-2-2-2000000220000020000000000000
χ2122222222-22-22-22-22-2-2222222000000000000-2-2000000-202-200000000000
χ2222222222-22-22-22-22-2-22222-2-2000000000000-2-200000020-2200000000000
χ2322222222-22-22-22-22-2-2-2-2-2-22200000000000022000000-20-2200000000000
χ2422222222-22-22-22-22-2-2-2-2-2-2-2-200000000000022000000202-200000000000
χ2522-22-2-2-22-202020-2000i2i2−i2−i200002-22-22-2i2i2−i2−i2i2−i200i2i2−i2−i200000000i2−i200000
χ2622-22-2-2-22-202020-2000i2i2−i2−i200002-2-22-22i2i2−i2−i2i2−i200−i2−i2i2i200000000−i2i200000
χ2722-22-2-2-22-202020-2000i2i2−i2−i20000-222-2-22−i2−i2i2i2i2−i200−i2−i2i2i200000000i2−i200000
χ2822-22-2-2-22-202020-2000i2i2−i2−i20000-22-222-2−i2−i2i2i2i2−i200i2i2−i2−i200000000−i2i200000
χ2922-22-2-2-22-202020-2000−i2−i2i2i200002-22-22-2−i2−i2i2i2−i2i200−i2−i2i2i200000000−i2i200000
χ3022-22-2-2-22-202020-2000−i2−i2i2i200002-2-22-22−i2−i2i2i2−i2i200i2i2−i2−i200000000i2−i200000
χ3122-22-2-2-22-202020-2000−i2−i2i2i20000-222-2-22i2i2−i2−i2−i2i200i2i2−i2−i200000000−i2i200000
χ3222-22-2-2-22-202020-2000−i2−i2i2i20000-22-222-2i2i2−i2−i2−i2i200−i2−i2i2i200000000i2−i200000
χ332-2-22-222-222-2-222-2-22-2000000000000002-22-20000000000002i−2i00002i−2i000
χ342-2-22-222-222-2-222-2-22-2000000000000002-22-2000000000000−2i2i0000−2i2i000
χ352-2-22-222-222-2-222-2-22-200000000000000-22-220000000000002i−2i0000−2i2i000
χ362-2-22-222-222-2-222-2-22-200000000000000-22-22000000000000−2i2i00002i−2i000
χ3744444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000
χ38444-4-44-4-404040-40-400000000000000000000000022−2222−22000000000000000
χ39444-4-44-4-404040-40-4000000000000000000000000−2222−2222000000000000000
χ40444-4-44-4-40-40-40404004i−4i4i−4i0000000000000000000000000000000000000
χ41444-4-44-4-40-40-4040400−4i4i−4i4i0000000000000000000000000000000000000
χ4244-44-4-4-4440-40-4040002i22i2−2i2−2i200000000000000−2i22i2000000000000000000000
χ4344-44-4-4-4440-40-404000−2i2−2i22i22i2000000000000002i2−2i2000000000000000000000
χ4444-4-44-44-4000000000022−22−222200000000000000002i2−2i22i−2i−2i2i000000000000000
χ4544-4-44-44-4000000000022−22−22220000000000000000−2i22i2−2i2i2i−2i000000000000000
χ4644-4-44-44-40000000000−222222−2200000000000000002i2−2i2−2i2i2i−2i000000000000000
χ4744-4-44-44-40000000000−222222−220000000000000000−2i22i22i−2i−2i2i000000000000000
χ484-4444-4-4-44040-40-40000000004-4000000000000000000000000000000000
χ494-4444-4-4-44040-40-4000000000-44000000000000000000000000000000000
χ504-4444-4-4-4-40-40404000000000000000002i2−2i2−2i22i200000000000000000000000
χ514-4444-4-4-4-40-4040400000000000000000−2i22i22i2−2i200000000000000000000000
χ524-4-44-444-44-4-444-4-44-4400000000000000000000000000000000000000000
χ534-4-44-444-4-444-4-444-4-4400000000000000000000000000000000000000000
χ544-4-44-444-4-4-444-4-4444-400000000000000000000000000000000000000000
χ554-4-4-444-44040-40-4040000004-400000000000000000000000000000000000
χ564-4-4-444-44040-40-404000000-4400000000000000000000000000000000000
χ574-4-4-444-440-404040-4000000000000000000000000000000000022−220000000
χ584-4-4-444-440-404040-40000000000000000000000000000000000−22220000000
χ598-88-8-8-888000000000000000000000000000000000000000000000000000

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