Finite Group Databasebeta

← Group #337969

Character table — Group #337969

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11111111222222224444448888888888888888888888161616161616161616161616323232
order12222222444444444488882244444488888888888888244444888888224
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-11-11
χ3111111111111111111111111-1-11111111111111111111-1-1-1-1-111-1-1-1-1-1-1-1
χ4111111111111111111111111-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-11-1
χ51111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1
χ61111111111111111111111-1-111-1-1-1-11111-1-1-1-1111111-1111-1-1-1-11111-1-1-1
χ71111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-11111111-11
χ81111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1111
χ9111111111111111111-1-1-1-111111111-1-111-1-1-1-111-1-1-1-111-1-111-1-1-1-1111-1-1
χ10111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-1-1-11111-1-111-1
χ11111111111111111111-1-1-1-111-1-11111-1-111-1-1-1-111-1-1-1-11-111-1-1-1-111-1-1-111
χ12111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-111-1-11
χ13111111111111111111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1111111-1-111-1-111-1-1-1-11
χ14111111111111111111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-11-1-1-1-111-1-111-111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111111-111-1-1-1-1-1-11111-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-11-1-1
χ17222222222-22-22-22-2-2-200002200-2-22200-2-20000220000-200000000000000
χ18222222222-22-22-22-2-2-200002200-2-2-2-200220000-2-20000200000000000000
χ19222222222-22-22-22-2-2-20000-2-200222200220000-2-20000-200000000000000
χ20222222222-22-22-22-2-2-20000-2-20022-2-200-2-20000220000200000000000000
χ2122222222-22-22-22-22-2-2222200220000-2-20000000000000-22-200000000000
χ2222222222-22-22-22-22-2-2222200-2-20000-2-200000000000002-2200000000000
χ2322222222-22-22-22-22-2-2-2-2-2-200220000220000000000000-2-2200000000000
χ2422222222-22-22-22-22-2-2-2-2-2-200-2-2000022000000000000022-200000000000
χ252222-2-2-2-2-202020-2000i2i2−i2−i22-200002i−2ii2−i200i2i2−i2−i22i−2i22−2−20000002−20000000
χ262222-2-2-2-2-202020-2000i2i2−i2−i22-20000−2i2ii2−i200i2i2−i2−i2−2i2i−2−222000000−220000000
χ272222-2-2-2-2-202020-2000i2i2−i2−i2-2200002i−2ii2−i200−i2−i2i2i2−2i2i−2−2220000002−20000000
χ282222-2-2-2-2-202020-2000i2i2−i2−i2-220000−2i2ii2−i200−i2−i2i2i22i−2i22−2−2000000−220000000
χ292222-2-2-2-2-202020-2000−i2−i2i2i22-200002i−2i−i2i200−i2−i2i2i22i−2i−2−222000000−220000000
χ302222-2-2-2-2-202020-2000−i2−i2i2i22-20000−2i2i−i2i200−i2−i2i2i2−2i2i22−2−20000002−20000000
χ312222-2-2-2-2-202020-2000−i2−i2i2i2-2200002i−2i−i2i200i2i2−i2−i2−2i2i22−2−2000000−220000000
χ322222-2-2-2-2-202020-2000−i2−i2i2i2-220000−2i2i−i2i200i2i2−i2−i22i−2i−2−2220000002−20000000
χ3322-2-2-222-222-2-222-2-22-200000000000000002i−2i2i−2i00000000002i−2i002-200000
χ3422-2-2-222-222-2-222-2-22-200000000000000002i−2i2i−2i0000000000−2i2i00-2200000
χ3522-2-2-222-222-2-222-2-22-20000000000000000−2i2i−2i2i00000000002i−2i00-2200000
χ3622-2-2-222-222-2-222-2-22-20000000000000000−2i2i−2i2i0000000000−2i2i002-200000
χ3744444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000
χ384444-4-4-4-440-40-4040002i22i2−2i2−2i200000000−2i22i2000000000000000000000000000
χ394444-4-4-4-440-40-404000−2i2−2i22i22i2000000002i2−2i2000000000000000000000000000
χ4044-4-44-4-444040-40-4000000000004i−4i0000000000000000000000000000000
χ4144-4-44-4-444040-40-400000000000−4i4i0000000000000000000000000000000
χ4244-4-44-4-44-40-40404000000000000000000022−22−2222000000000000000000000
χ4344-4-44-4-44-40-404040000000000000000000−222222−22000000000000000000000
χ4444-4-4-444-44-4-444-4-44-4400000000000000000000000000000000000000000
χ4544-4-4-444-4-444-4-444-4-4400000000000000000000000000000000000000000
χ4644-4-4-444-4-4-444-4-4444-400000000000000000000000000000000000000000
χ474-44-444-4-404040-40-4004i−4i4i−4i0000000000000000000000000000000000000
χ484-44-444-4-404040-40-400−4i4i−4i4i0000000000000000000000000000000000000
χ494-44-444-4-40-40-4040400000000000000000000000022−2222−22000000000000000
χ504-44-444-4-40-40-40404000000000000000000000000−2222−2222000000000000000
χ514-44-4-4-444000000000022−22−2222000000000022−220000002-2-22000000000000000
χ524-44-4-4-444000000000022−22−22220000000000−2222000000-222-2000000000000000
χ534-44-4-4-4440000000000−222222−22000000000022−22000000-222-2000000000000000
χ544-44-4-4-4440000000000−222222−220000000000−22220000002-2-22000000000000000
χ554-4-44-44-44040-40-4040000000000000000000000000000000000000022−22000
χ564-4-44-44-44040-40-40400000000000000000000000000000000000000−2222000
χ574-4-44-44-440-404040-4000000004-4000000000000000000000000000000000
χ584-4-44-44-440-404040-400000000-44000000000000000000000000000000000
χ598-8-888-88-8000000000000000000000000000000000000000000000000000

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