Finite Group Databasebeta

← Group #310352

Character table — Group #310352

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888444444444488888888888888244444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-111111-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-111-1
χ411111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-11
χ51111111111111111111111-1-1-1-111-1-1111111-1-11111-1-1-1-1-1-1-1-1111-1-1-11111-1-1-1-1-1
χ61111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-1-1-1-111111
χ71111111111111111111111-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-11-1-1111-1-1-1-111-1-11
χ81111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11111111-1-111-1
χ911111111111111111-1-1-1-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111-1-1-1-1111
χ1011111111111111111-1-1-1-1111111111-1-111-1-1111111-1-1-1-11111-1-1-1-1-11-1-11111-1-1-1
χ1111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1111111-1
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-11111-111-1-1-1-1-1-11
χ1311111111111111111-1-1-1-11-1-1-1-111-1-1-1-11111-1-1-1-1-1-1111111111-1-111-111-1-111-1-1-1
χ1411111111111111111-1-1-1-11-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-111-1-1-111-1-1111
χ1511111111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-111111111111-1-11-1-111-1-1-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-1111-1-11111-1
χ17222222222-22-2-222-2-22222-200000000-2-2002200-2-22200000000-200000000000000
χ18222222222-22-2-222-2-22222-200000000-2-200-2-20022-2-200000000200000000000000
χ19222222222-22-2-222-2-2-2-2-2-2-2000000002200220022-2-200000000-200000000000000
χ20222222222-22-2-222-2-2-2-2-2-2-2000000002200-2-200-2-22200000000200000000000000
χ2122222222-22-222-2-22-20000-22222222200-2-200-2-200000000000000000-2000000000
χ2222222222-22-222-2-22-20000-22222-2-2-2-2002200-2-2000000000000000002000000000
χ2322222222-22-222-2-22-20000-2-2-2-2-222-2-200-2-20022000000000000000002000000000
χ2422222222-22-222-2-22-20000-2-2-2-2-2-2-2220022002200000000000000000-2000000000
χ2522-2-22-2-22-202002-20022-2-20i2i2−i2−i2000000002i−2ii2−i2002i−2ii2i2−i2−i222−2−20000000000002−20
χ2622-2-22-2-22-202002-20022-2-20i2i2−i2−i200000000−2i2ii2−i200−2i2ii2i2−i2−i2−2−222000000000000−220
χ2722-2-22-2-22-202002-20022-2-20−i2−i2i2i2000000002i−2i−i2i2002i−2i−i2−i2i2i2−2−222000000000000−220
χ2822-2-22-2-22-202002-20022-2-20−i2−i2i2i200000000−2i2i−i2i200−2i2i−i2−i2i2i222−2−20000000000002−20
χ2922-2-22-2-22-202002-200-2-2220i2i2−i2−i2000000002i−2ii2−i200−2i2i−i2−i2i2i2−2−2220000000000002−20
χ3022-2-22-2-22-202002-200-2-2220i2i2−i2−i200000000−2i2ii2−i2002i−2i−i2−i2i2i222−2−2000000000000−220
χ3122-2-22-2-22-202002-200-2-2220−i2−i2i2i2000000002i−2i−i2i200−2i2ii2i2−i2−i222−2−2000000000000−220
χ3222-2-22-2-22-202002-200-2-2220−i2−i2i2i200000000−2i2i−i2i2002i−2ii2i2−i2−i2−2−2220000000000002−20
χ332-2-2-2222-222-2-2-22-2222i−2i2i−2i-2000000002i−2i0000000000000000000000002i−2i2-200000
χ342-2-2-2222-222-2-2-22-2222i−2i2i−2i-2000000002i−2i000000000000000000000000−2i2i-2200000
χ352-2-2-2222-222-2-2-22-222−2i2i−2i2i-200000000−2i2i0000000000000000000000002i−2i-2200000
χ362-2-2-2222-222-2-2-22-222−2i2i−2i2i-200000000−2i2i000000000000000000000000−2i2i2-200000
χ372-2-2-2222-22-2-2222-2-2-22i−2i2i−2i200002i−2i00−2i2i2i−2i000000000000000002-2000000000000
χ382-2-2-2222-22-2-2222-2-2-22i−2i2i−2i20000−2i2i00−2i2i−2i2i00000000000000000-22000000000000
χ392-2-2-2222-22-2-2222-2-2-2−2i2i−2i2i200002i−2i002i−2i2i−2i00000000000000000-22000000000000
χ402-2-2-2222-22-2-2222-2-2-2−2i2i−2i2i20000−2i2i002i−2i−2i2i000000000000000002-2000000000000
χ412-2-2-2222-2-2-2222-22-220000-200002i−2i0000−2i2i000000002i−2i2i−2i00000002-20000000000
χ422-2-2-2222-2-2-2222-22-220000-200002i−2i0000−2i2i00000000−2i2i−2i2i0000000-220000000000
χ432-2-2-2222-2-2-2222-22-220000-20000−2i2i00002i−2i000000002i−2i2i−2i0000000-220000000000
χ442-2-2-2222-2-2-2222-22-220000-20000−2i2i00002i−2i00000000−2i2i−2i2i00000002-20000000000
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000
χ46444-4-4-44-40404-400-40000000000004-400000000000000000000000000000000000
χ47444-4-4-44-40404-400-4000000000000-4400000000000000000000000000000000000
χ48444-4-4-44-40-40-44004000000000000000000000000000000000000000000002i2−2i2000
χ49444-4-4-44-40-40-4400400000000000000000000000000000000000000000000−2i22i2000
χ5044-4-44-4-4440-400-4400000002i22i2−2i2−2i20000000000−2i22i2000000000000000000000000000
χ5144-4-44-4-4440-400-440000000−2i2−2i22i22i200000000002i2−2i2000000000000000000000000000
χ524-4444-4-4-440400-4-400000000000000000000000000022−22−22220000000000000000000
χ534-4444-4-4-440400-4-4000000000000000000000000000−222222−220000000000000000000
χ544-4444-4-4-4-40-40044004i−4i−4i4i00000000000000000000000000000000000000000000
χ554-4444-4-4-4-40-4004400−4i4i4i−4i00000000000000000000000000000000000000000000
χ564-44-4-44-44000000000000002i2−2i22i2−2i200000000000022−220000002i−2i2i−2i000000000000000
χ574-44-4-44-44000000000000002i2−2i22i2−2i2000000000000−2222000000−2i2i−2i2i000000000000000
χ584-44-4-44-4400000000000000−2i22i2−2i22i200000000000022−22000000−2i2i−2i2i000000000000000
χ594-44-4-44-4400000000000000−2i22i2−2i22i2000000000000−22220000002i−2i2i−2i000000000000000
χ604-4-44-4-444040-4400-40000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ614-4-44-4-444040-4400-4000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ624-4-44-4-4440-404-40040000004-4-44000000000000000000000000000000000000000
χ634-4-44-4-4440-404-4004000000-444-4000000000000000000000000000000000000000
χ644-4-4-4444-4-444-4-4-444-4000040000000000000000000000000000000000000000000
χ6588-88-88-8-8000000000000000000000000000000000000000000000000000000000

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