Finite Group Databasebeta

← Group #313913

Character table — Group #313913

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444444444448888888844444444448888888888888888222444888824
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-11111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1111-1-1-111-1-11-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1111-1-111-11
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111111-1-1-1-1-111-11
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-111111-1-11-1
χ911111111111111111-1-1-1-111111111111-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-111
χ1011111111111111111-1-1-1-111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111-1111111-1-1
χ1111111111111111111-1-1-1-1111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111111-1-11-1-11111-1-1
χ1211111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-111-111-1-1-1-111
χ1311111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111111-1-1-111-1-1111-1
χ1411111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-11111-1111-1-111-1-1-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-11-1-1-11111-1-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1111-1-1-1-1111-1
χ17222222222-22-22-22-2-20000-22222-2-2-2-200002200220000000000000000-200-200000000
χ18222222222-22-22-22-2-20000-22222-2-2-2-20000-2-200-2-20000000000000000200200000000
χ19222222222-22-22-22-2-20000-2-2-2-2-2222200002200-2-20000000000000000-200200000000
χ20222222222-22-22-22-2-20000-2-2-2-2-222220000-2-200220000000000000000200-200000000
χ2122222222-22-22-22-22-22222-20000000022-2-200-2-2002200000000-2-20000000000000000
χ2222222222-22-22-22-22-22222-200000000-2-2-2-2002200-2-200000000220000000000000000
χ2322222222-22-22-22-22-2-2-2-2-2-200000000222200-2-200-2-200000000220000000000000000
χ2422222222-22-22-22-22-2-2-2-2-2-200000000-2-2220022002200000000-2-20000000000000000
χ2522-22-22-2-20-202020-2022-2-20i2i2−i2−i2i2i2−i2−i22-2000000002-2i2i2−i2−i2i2i2−i2−i200i2i2−i2−i2000000000000
χ2622-22-22-2-20-202020-2022-2-20i2i2−i2−i2i2i2−i2−i2-2200000000-22−i2−i2i2i2i2i2−i2−i200−i2−i2i2i2000000000000
χ2722-22-22-2-20-202020-2022-2-20−i2−i2i2i2−i2−i2i2i22-2000000002-2−i2−i2i2i2−i2−i2i2i200−i2−i2i2i2000000000000
χ2822-22-22-2-20-202020-2022-2-20−i2−i2i2i2−i2−i2i2i2-2200000000-22i2i2−i2−i2−i2−i2i2i200i2i2−i2−i2000000000000
χ2922-22-22-2-20-202020-20-2-2220i2i2−i2−i2i2i2−i2−i22-200000000-22i2i2−i2−i2−i2−i2i2i200−i2−i2i2i2000000000000
χ3022-22-22-2-20-202020-20-2-2220i2i2−i2−i2i2i2−i2−i2-22000000002-2−i2−i2i2i2−i2−i2i2i200i2i2−i2−i2000000000000
χ3122-22-22-2-20-202020-20-2-2220−i2−i2i2i2−i2−i2i2i22-200000000-22−i2−i2i2i2i2i2−i2−i200i2i2−i2−i2000000000000
χ3222-22-22-2-20-202020-20-2-2220−i2−i2i2i2−i2−i2i2i2-22000000002-2i2i2−i2−i2i2i2−i2−i200−i2−i2i2i2000000000000
χ332-22-222-2-222-2-222-2-2-22-22-222i−2i2i−2i2i−2i2i−2i002-20000000000002i−2i2i−2i000000000000000000
χ342-22-222-2-222-2-222-2-2-22-22-22−2i2i−2i2i−2i2i−2i2i002-2000000000000−2i2i−2i2i000000000000000000
χ352-22-222-2-222-2-222-2-2-2-22-2222i−2i2i−2i2i−2i2i−2i00-22000000000000−2i2i−2i2i000000000000000000
χ362-22-222-2-222-2-222-2-2-2-22-222−2i2i−2i2i−2i2i−2i2i00-220000000000002i−2i2i−2i000000000000000000
χ372-22-222-2-22-2-222-2-2220000-22i−2i2i−2i−2i2i−2i2i0000000000000000000000000002-202i−2i000000
χ382-22-222-2-22-2-222-2-2220000-22i−2i2i−2i−2i2i−2i2i000000000000000000000000000-220−2i2i000000
χ392-22-222-2-22-2-222-2-2220000-2−2i2i−2i2i2i−2i2i−2i0000000000000000000000000002-20−2i2i000000
χ402-22-222-2-22-2-222-2-2220000-2−2i2i−2i2i2i−2i2i−2i000000000000000000000000000-2202i−2i000000
χ412-22-222-2-2-222-2-222-222-22-2-20000000000-22000000002i−2i2i−2i0000002i−2i2i−2i000000000000
χ422-22-222-2-2-222-2-222-222-22-2-20000000000-2200000000−2i2i−2i2i000000−2i2i−2i2i000000000000
χ432-22-222-2-2-222-2-222-22-22-22-200000000002-2000000002i−2i2i−2i000000−2i2i−2i2i000000000000
χ442-22-222-2-2-222-2-222-22-22-22-200000000002-200000000−2i2i−2i2i0000002i−2i2i−2i000000000000
χ452-2-2-2-22220-20-2020202-2-2202−2−222−2−220000002-200002−2−222−2−222-22−2−22000000000000
χ462-2-2-2-22220-20-2020202-2-2202−2−222−2−22000000-220000−222−22−2−22-22−222−2000000000000
χ472-2-2-2-22220-20-2020202-2-220−222−2−222−20000002-20000−222−2−222−22-2−222−2000000000000
χ482-2-2-2-22220-20-2020202-2-220−222−2−222−2000000-2200002−2−22−222−2-222−2−22000000000000
χ492-2-2-2-22220-20-202020-222-202−2−222−2−220000002-200002−2−22−222−2-22−222−2000000000000
χ502-2-2-2-22220-20-202020-222-202−2−222−2−22000000-220000−222−2−222−22-22−2−22000000000000
χ512-2-2-2-22220-20-202020-222-20−222−2−222−20000002-20000−222−22−2−22-222−2−22000000000000
χ522-2-2-2-22220-20-202020-222-20−222−2−222−2000000-2200002−2−222−2−222-2−222−2000000000000
χ5344444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000000
χ54444-4-4-44-440-40-404000000000000000000000000000000000000000000000002i2−2i20000
χ55444-4-4-44-440-40-40400000000000000000000000000000000000000000000000−2i22i20000
χ56444-4-4-44-4-404040-400000000000000000004i−4i00000000000000000000000000000000
χ57444-4-4-44-4-404040-40000000000000000000−4i4i00000000000000000000000000000000
χ5844-44-44-4-4040-40-4040000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000000000000000
χ5944-44-44-4-4040-40-404000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000000000000000
χ604-444-4-4-444040-40-400000000000000000000000000000000000000000000000002i2−2i200
χ614-444-4-4-444040-40-40000000000000000000000000000000000000000000000000−2i22i200
χ624-444-4-4-44-40-40404000000000000000000000004-40000000000000000000000000000
χ634-444-4-4-44-40-4040400000000000000000000000-440000000000000000000000000000
χ644-44-444-4-4-4-444-4-444-4000040000000000000000000000000000000000000000000000
χ654-4-4-4-444404040-40-400000022−22−2222−222222−2200000000000000000000000000000000000000
χ664-4-4-4-444404040-40-4000000−222222−2222−22−222200000000000000000000000000000000000000
χ6788-8-88-8-88000000000000000000000000000000000000000000000000000000000000
χ688-8-888-88-8000000000000000000000000000000000000000000000000000000000000

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