Finite Group Databasebeta

← Group #305683

Character table — Group #305683

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888222244444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1111-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111111
χ51111111111111111111111-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-1-11111-1-11-1-111-1-1-1
χ61111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-111-1-1111
χ71111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11-1-1-1-1111-1-1-1-1111
χ81111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-111-11111-1-1-1
χ911111111111111111-1-1-1-111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111-1-1-1-11
χ1011111111111111111-1-1-1-111111-1-1111111-1-111-1-1-1-1111111111-1-1-1-1-1-1-1-1-11111-1
χ1111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1111111-1-1-1-1-1-1-11
χ1311111111111111111-1-1-1-11-1-1-1-1-1-11111-1-111-1-11111-1-1-1-11111-111-1-1111-1-1-1-111-1
χ1411111111111111111-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-11111-1-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111111-1-111-1-11-1-111-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111111-1-1-111-1-111-1
χ172222222222-2-222-2-2-22222-20000-2-20000002200000022-2-200000000000-20000000
χ182222222222-2-222-2-2-22222-20000-2-2000000-2-2000000-2-2220000000000020000000
χ192222222222-2-222-2-2-2-2-2-2-2-200002200000022000000-2-22200000000000-20000000
χ202222222222-2-222-2-2-2-2-2-2-2-2000022000000-2-200000022-2-20000000000020000000
χ2122222222-2-222-2-222-20000-222220022-2-22200-2-2000000000000-200000000000000
χ2222222222-2-222-2-222-20000-2222200-2-222-2-200-2-2000000000000200000000000000
χ2322222222-2-222-2-222-20000-2-2-2-2-20022-2-2-2-20022000000000000200000000000000
χ2422222222-2-222-2-222-20000-2-2-2-2-200-2-222220022000000000000-200000000000000
χ2522-22-2-2-222-2002-20002i2i−2i−2i0i2i2−i2−i2000000002i−2ii2−i222−2−22-200i2i2−i2−i2000000002−200000
χ2622-22-2-2-222-2002-20002i2i−2i−2i0i2i2−i2−i200000000−2i2ii2−i222−2−2-2200−i2−i2i2i200000000−2200000
χ2722-22-2-2-222-2002-20002i2i−2i−2i0−i2−i2i2i2000000002i−2i−i2i2−2−2222-200−i2−i2i2i200000000−2200000
χ2822-22-2-2-222-2002-20002i2i−2i−2i0−i2−i2i2i200000000−2i2i−i2i2−2−222-2200i2i2−i2−i2000000002−200000
χ2922-22-2-2-222-2002-2000−2i−2i2i2i0i2i2−i2−i2000000002i−2ii2−i2−2−222-2200−i2−i2i2i2000000002−200000
χ3022-22-2-2-222-2002-2000−2i−2i2i2i0i2i2−i2−i200000000−2i2ii2−i2−2−2222-200i2i2−i2−i200000000−2200000
χ3122-22-2-2-222-2002-2000−2i−2i2i2i0−i2−i2i2i2000000002i−2i−i2i222−2−2-2200i2i2−i2−i200000000−2200000
χ3222-22-2-2-222-2002-2000−2i−2i2i2i0−i2−i2i2i200000000−2i2i−i2i222−2−22-200−i2−i2i2i2000000002−200000
χ332-222-2-22-22222-2-2-2-222-22-2-200002-22-22-20000000000000000000002-20000000000
χ342-222-2-22-22222-2-2-2-222-22-2-200002-2-22-22000000000000000000000-220000000000
χ352-222-2-22-22222-2-2-2-22-22-22-20000-222-22-2000000000000000000000-220000000000
χ362-222-2-22-22222-2-2-2-22-22-22-20000-22-22-220000000000000000000002-20000000000
χ372-222-2-22-222-2-2-2-222-22-22-220000-22000000000000000000000002i−2i00000002i−2i000
χ382-222-2-22-222-2-2-2-222-22-22-220000-2200000000000000000000000−2i2i0000000−2i2i000
χ392-222-2-22-222-2-2-2-222-2-22-22200002-2000000000000000000000002i−2i0000000−2i2i000
χ402-222-2-22-222-2-2-2-222-2-22-22200002-200000000000000000000000−2i2i00000002i−2i000
χ412-222-2-22-2-2-22222-2-2-2000020000002-2-220000002i−2i2i−2i00000000000002i−2i00000000
χ422-222-2-22-2-2-22222-2-2-2000020000002-2-22000000−2i2i−2i2i0000000000000−2i2i00000000
χ432-222-2-22-2-2-22222-2-2-200002000000-222-20000002i−2i2i−2i0000000000000−2i2i00000000
χ442-222-2-22-2-2-22222-2-2-200002000000-222-2000000−2i2i−2i2i00000000000002i−2i00000000
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000
χ46444-44-4-4-40000000000000022−2222−2200000000000000000022−222-22-2000000000000000
χ47444-44-4-4-40000000000000022−2222−22000000000000000000−2222-22-22000000000000000
χ48444-44-4-4-400000000000000−2222−222200000000000000000022−22-22-22000000000000000
χ49444-44-4-4-400000000000000−2222−2222000000000000000000−22222-22-2000000000000000
χ5044-44-4-4-44-4400-44000000002i22i2−2i2−2i20000000000−2i22i2000000000000000000000000000
χ5144-44-4-4-44-4400-4400000000−2i2−2i22i22i200000000002i2−2i2000000000000000000000000000
χ5244-4-4-444-4004-4004-40000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ5344-4-4-444-4004-4004-4000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ5444-4-4-444-400-4400-440000004i−4i−4i4i000000000000000000000000000000000000000
χ5544-4-4-444-400-4400-44000000−4i4i4i−4i000000000000000000000000000000000000000
χ564-444-4-44-4-4-4-4-4444440000-40000000000000000000000000000000000000000000
χ574-4-4444-4-44-400-440004i−4i−4i4i00000000000000000000000000000000000000000000
χ584-4-4444-4-44-400-44000−4i4i4i−4i00000000000000000000000000000000000000000000
χ594-4-4444-4-4-44004-40000000000000000000000002i2−2i2−2i22i200000000000000000000000
χ604-4-4444-4-4-44004-4000000000000000000000000−2i22i22i2−2i200000000000000000000000
χ614-4-4-44-444004-400-44000000000000000000000000000000000000000000000022−220
χ624-4-4-44-444004-400-440000000000000000000000000000000000000000000000−22220
χ634-4-4-44-44400-44004-400000000000000004-40000000000000000000000000000000
χ644-4-4-44-44400-44004-40000000000000000-440000000000000000000000000000000
χ658-88-8-88-88000000000000000000000000000000000000000000000000000000000

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