Finite Group Databasebeta

← Group #312849

Character table — Group #312849

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444444444448888888822444444448888888888888888444444888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-11111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-111-1-1111-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1111-1-111-1-1-11
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-11111-1-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1111-1-1-1-1111-1
χ911111111111111111-1-1-1-111111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111
χ1011111111111111111-1-1-1-111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1
χ1111111111111111111-1-1-1-1111111111-1-1-1-111-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1
χ1211111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-111
χ1311111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111111-111-1-111-1-11-1
χ1411111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1-1-11111-11-1-111-1-111-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-11-111-1-1-1-111-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-11-1-11111-1-11-1
χ17222222222-22-22-22-2-22222-20000000022-2-200-2-200-2-200002200000000000000000000
χ18222222222-22-22-22-2-22222-200000000-2-2-2-2002200220000-2-200000000000000000000
χ19222222222-22-22-22-2-2-2-2-2-2-200000000222200-2-200220000-2-200000000000000000000
χ20222222222-22-22-22-2-2-2-2-2-2-200000000-2-222002200-2-200002200000000000000000000
χ2122222222-22-22-22-22-20000-22222-2-2-2-200002200220000000000000000-2-20000000000
χ2222222222-22-22-22-22-20000-22222-2-2-2-20000-2-200-2-20000000000000000220000000000
χ2322222222-22-22-22-22-20000-2-2-2-2-2222200002200-2-20000000000000000-220000000000
χ2422222222-22-22-22-22-20000-2-2-2-2-222220000-2-2002200000000000000002-20000000000
χ2522-2-222-2-2-20-202020022-2-2022−2−222−2−20000002i−2i002i−2i22−2−200i2i2−i2−i2i2i2−i2−i2000000000000
χ2622-2-222-2-2-20-202020022-2-2022−2−222−2−2000000−2i2i00−2i2i22−2−200−i2−i2i2i2−i2−i2i2i2000000000000
χ2722-2-222-2-2-20-202020022-2-20−2−222−2−2220000002i−2i002i−2i−2−22200−i2−i2i2i2−i2−i2i2i2000000000000
χ2822-2-222-2-2-20-202020022-2-20−2−222−2−222000000−2i2i00−2i2i−2−22200i2i2−i2−i2i2i2−i2−i2000000000000
χ2922-2-222-2-2-20-2020200-2-222022−2−222−2−20000002i−2i00−2i2i−2−22200i2i2−i2−i2−i2−i2i2i2000000000000
χ3022-2-222-2-2-20-2020200-2-222022−2−222−2−2000000−2i2i002i−2i−2−22200−i2−i2i2i2i2i2−i2−i2000000000000
χ3122-2-222-2-2-20-2020200-2-2220−2−222−2−2220000002i−2i00−2i2i22−2−200−i2−i2i2i2i2i2−i2−i2000000000000
χ3222-2-222-2-2-20-2020200-2-2220−2−222−2−222000000−2i2i002i−2i22−2−200i2i2−i2−i2−i2−i2i2i2000000000000
χ332-22-22-22-2-202020-2002i−2i2i−2i0i2−i2i2−i2i2−i2i2−i22-200000000002−22−22i−2ii2−i2i2−i22−22−2000000000000
χ342-22-22-22-2-202020-2002i−2i2i−2i0i2−i2i2−i2i2−i2i2−i2-2200000000002−22−2−2i2i−i2i2−i2i2−22−22000000000000
χ352-22-22-22-2-202020-2002i−2i2i−2i0−i2i2−i2i2−i2i2−i2i22-20000000000−22−222i−2i−i2i2−i2i2−22−22000000000000
χ362-22-22-22-2-202020-2002i−2i2i−2i0−i2i2−i2i2−i2i2−i2i2-220000000000−22−22−2i2ii2−i2i2−i22−22−2000000000000
χ372-22-22-22-2-202020-200−2i2i−2i2i0i2−i2i2−i2i2−i2i2−i22-20000000000−22−22−2i2ii2−i2i2−i2−22−22000000000000
χ382-22-22-22-2-202020-200−2i2i−2i2i0i2−i2i2−i2i2−i2i2−i2-220000000000−22−222i−2i−i2i2−i2i22−22−2000000000000
χ392-22-22-22-2-202020-200−2i2i−2i2i0−i2i2−i2i2−i2i2−i2i22-200000000002−22−2−2i2i−i2i2−i2i22−22−2000000000000
χ402-22-22-22-2-202020-200−2i2i−2i2i0−i2i2−i2i2−i2i2−i2i2-2200000000002−22−22i−2ii2−i2i2−i2−22−22000000000000
χ412-2-222-2-2222-2-222-2-2-22i−2i−2i2i22i−2i−2i2i2i−2i−2i2i002i−2i000000002-2-220000000000000000000000
χ422-2-222-2-2222-2-222-2-2-22i−2i−2i2i2−2i2i2i−2i−2i2i2i−2i002i−2i00000000-222-20000000000000000000000
χ432-2-222-2-2222-2-222-2-2-2−2i2i2i−2i22i−2i−2i2i2i−2i−2i2i00−2i2i00000000-222-20000000000000000000000
χ442-2-222-2-2222-2-222-2-2-2−2i2i2i−2i2−2i2i2i−2i−2i2i2i−2i00−2i2i000000002-2-220000000000000000000000
χ452-2-222-2-222-2-222-2-2222i−2i−2i2i-20000000000−2i2i000000000000002-2-22−2i2i2i−2i000000000000
χ462-2-222-2-222-2-222-2-2222i−2i−2i2i-20000000000−2i2i00000000000000-222-22i−2i−2i2i000000000000
χ472-2-222-2-222-2-222-2-222−2i2i2i−2i-200000000002i−2i000000000000002-2-222i−2i−2i2i000000000000
χ482-2-222-2-222-2-222-2-222−2i2i2i−2i-200000000002i−2i00000000000000-222-2−2i2i2i−2i000000000000
χ492-2-222-2-22-222-2-222-220000-22i−2i−2i2i−2i2i2i−2i00000000000000000000000000002i−2i2-2000000
χ502-2-222-2-22-222-2-222-220000-22i−2i−2i2i−2i2i2i−2i0000000000000000000000000000−2i2i-22000000
χ512-2-222-2-22-222-2-222-220000-2−2i2i2i−2i2i−2i−2i2i00000000000000000000000000002i−2i-22000000
χ522-2-222-2-22-222-2-222-220000-2−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000−2i2i2-2000000
χ5344444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000000
χ54444-4-4-4-4404040-40-400000000000000000000000000000000000000000000000022−2200
χ55444-4-4-4-4404040-40-4000000000000000000000000000000000000000000000000−222200
χ56444-4-4-4-440-40-404040000000000000000004i−4i00000000000000000000000000000000
χ57444-4-4-4-440-40-40404000000000000000000−4i4i00000000000000000000000000000000
χ5844-4-444-4-44040-40-400000002222−22−22−22−22222200000000000000000000000000000000000000
χ5944-4-444-4-44040-40-40000000−22−2222222222−22−2200000000000000000000000000000000000000
χ604-44-44-44-440-40-40400000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000000000
χ614-44-44-44-440-40-4040000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000000000
χ624-4-444-4-44-4-444-4-444-4000040000000000000000000000000000000000000000000000
χ634-4-4-4-4444040-40-404000000000000000000000000000000000000000000000022−220000
χ644-4-4-4-4444040-40-4040000000000000000000000000000000000000000000000−22220000
χ654-4-4-4-44440-404040-400000000000000000000004-40000000000000000000000000000
χ664-4-4-4-44440-404040-40000000000000000000000-440000000000000000000000000000
χ6788-88-8-88-8000000000000000000000000000000000000000000000000000000000000
χ688-888-88-8-8000000000000000000000000000000000000000000000000000000000000

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