Finite Group Databasebeta

← Group #312813

Character table — Group #312813

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444444444448888888822444444448888888888888888444444888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ3111111111111111111111111111111-1-11111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1111-1-111-1-11-1
χ61111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1111-1-1-1-111-11
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-111-1-111-11
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111111-1-1-11111-1-11-1
χ911111111111111111-1-1-1-11111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111
χ1011111111111111111-1-1-1-111111111111-1-1-1-111-1-111-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1
χ1111111111111111111-1-1-1-1111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1
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
χ1311111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-11111-11-1-111-1-1111-1
χ1411111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11-1-11111-1-1-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1-1-111111-111-1-111-1-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-11-111-1-1-1-1111-1
χ17222222222-22-22-22-2-22222-2000000000022-2-200-2-2-2-200002200000000000000000000
χ18222222222-22-22-22-2-22222-20000000000-2-2-2-20022220000-2-200000000000000000000
χ19222222222-22-22-22-2-2-2-2-2-2-20000000000222200-2-2220000-2-200000000000000000000
χ20222222222-22-22-22-2-2-2-2-2-2-20000000000-2-2220022-2-200002200000000000000000000
χ2122222222-22-22-22-22-20000-22222-2-2-2-2220000-2-20000000000000000002-20000000000
χ2222222222-22-22-22-22-20000-22222-2-2-2-2-2-2000022000000000000000000-220000000000
χ2322222222-22-22-22-22-20000-2-2-2-2-2222222000022000000000000000000-2-20000000000
χ2422222222-22-22-22-22-20000-2-2-2-2-22222-2-20000-2-2000000000000000000220000000000
χ2522-22-22-2-2-20-20202002i2i−2i−2i022−2−222−2−2002i−2i00000000i2i2−i2−i22-2i2i2−i2−i222−2−2000000000000
χ2622-22-22-2-2-20-20202002i2i−2i−2i022−2−222−2−200−2i2i00000000i2i2−i2−i2-22−i2−i2i2i2−2−222000000000000
χ2722-22-22-2-2-20-20202002i2i−2i−2i0−2−222−2−222002i−2i00000000−i2−i2i2i22-2−i2−i2i2i2−2−222000000000000
χ2822-22-22-2-2-20-20202002i2i−2i−2i0−2−222−2−22200−2i2i00000000−i2−i2i2i2-22i2i2−i2−i222−2−2000000000000
χ2922-22-22-2-2-20-2020200−2i−2i2i2i022−2−222−2−2002i−2i00000000−i2−i2i2i2-22i2i2−i2−i2−2−222000000000000
χ3022-22-22-2-2-20-2020200−2i−2i2i2i022−2−222−2−200−2i2i00000000−i2−i2i2i22-2−i2−i2i2i222−2−2000000000000
χ3122-22-22-2-2-20-2020200−2i−2i2i2i0−2−222−2−222002i−2i00000000i2i2−i2−i2-22−i2−i2i2i222−2−2000000000000
χ3222-22-22-2-2-20-2020200−2i−2i2i2i0−2−222−2−22200−2i2i00000000i2i2−i2−i22-2i2i2−i2−i2−2−222000000000000
χ332-22-2-22-2222-2-222-2-2-22i−2i2i−2i22i−2i2i−2i2i−2i2i−2i00002i−2i0000002-22-20000000000000000000000
χ342-22-2-22-2222-2-222-2-2-22i−2i2i−2i2−2i2i−2i2i−2i2i−2i2i00002i−2i000000-22-220000000000000000000000
χ352-22-2-22-2222-2-222-2-2-2−2i2i−2i2i22i−2i2i−2i2i−2i2i−2i0000−2i2i000000-22-220000000000000000000000
χ362-22-2-22-2222-2-222-2-2-2−2i2i−2i2i2−2i2i−2i2i−2i2i−2i2i0000−2i2i0000002-22-20000000000000000000000
χ372-22-2-22-222-2-222-2-2222i−2i2i−2i-2000000000000−2i2i0000000000002-22-22i−2i2i−2i000000000000
χ382-22-2-22-222-2-222-2-2222i−2i2i−2i-2000000000000−2i2i000000000000-22-22−2i2i−2i2i000000000000
χ392-22-2-22-222-2-222-2-222−2i2i−2i2i-20000000000002i−2i0000000000002-22-2−2i2i−2i2i000000000000
χ402-22-2-22-222-2-222-2-222−2i2i−2i2i-20000000000002i−2i000000000000-22-222i−2i2i−2i000000000000
χ412-22-2-22-22-222-2-222-220000-22i−2i2i−2i−2i2i−2i2i00000000000000000000000000002i−2i2-2000000
χ422-22-2-22-22-222-2-222-220000-22i−2i2i−2i−2i2i−2i2i0000000000000000000000000000−2i2i-22000000
χ432-22-2-22-22-222-2-222-220000-2−2i2i−2i2i2i−2i2i−2i00000000000000000000000000002i−2i-22000000
χ442-22-2-22-22-222-2-222-220000-2−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000−2i2i2-2000000
χ452-2-2-2222-2-202020-2002-2-220i2−i2−i2i2i2−i2−i2i2000000002-22-2−i2i2i2−i200i2−i2−i2i2−i2i2i2−i2000000000000
χ462-2-2-2222-2-202020-2002-2-220i2−i2−i2i2i2−i2−i2i200000000-22-22−i2i2i2−i200−i2i2i2−i2i2−i2−i2i2000000000000
χ472-2-2-2222-2-202020-2002-2-220−i2i2i2−i2−i2i2i2−i2000000002-22-2i2−i2−i2i200−i2i2i2−i2i2−i2−i2i2000000000000
χ482-2-2-2222-2-202020-2002-2-220−i2i2i2−i2−i2i2i2−i200000000-22-22i2−i2−i2i200i2−i2−i2i2−i2i2i2−i2000000000000
χ492-2-2-2222-2-202020-200-222-20i2−i2−i2i2i2−i2−i2i2000000002-2-22i2−i2−i2i200i2−i2−i2i2i2−i2−i2i2000000000000
χ502-2-2-2222-2-202020-200-222-20i2−i2−i2i2i2−i2−i2i200000000-222-2i2−i2−i2i200−i2i2i2−i2−i2i2i2−i2000000000000
χ512-2-2-2222-2-202020-200-222-20−i2i2i2−i2−i2i2i2−i2000000002-2-22−i2i2i2−i200−i2i2i2−i2−i2i2i2−i2000000000000
χ522-2-2-2222-2-202020-200-222-20−i2i2i2−i2−i2i2i2−i200000000-222-2−i2i2i2−i200i2−i2−i2i2i2−i2−i2i2000000000000
χ5344444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000000
χ5444-44-44-4-44040-40-400000002222−22−22−22−22222200000000000000000000000000000000000000
χ5544-44-44-4-44040-40-40000000−22−2222222222−22−2200000000000000000000000000000000000000
χ5644-4-44-4-44040-40-4040000000000000000000000000000000000000000000000002i2−2i200
χ5744-4-44-4-44040-40-404000000000000000000000000000000000000000000000000−2i22i200
χ5844-4-44-4-440-404040-4000000000000000000004i−4i000000000000000000000000000000
χ5944-4-44-4-440-404040-400000000000000000000−4i4i000000000000000000000000000000
χ604-44-4-44-44-4-444-4-444-4000040000000000000000000000000000000000000000000000
χ614-4-44-4-44404040-40-400000000000000000000000000000000000000000000002i2−2i20000
χ624-4-44-4-44404040-40-40000000000000000000000000000000000000000000000−2i22i20000
χ634-4-44-4-4440-40-40404000000000000004-4000000000000000000000000000000000000
χ644-4-44-4-4440-40-4040400000000000000-44000000000000000000000000000000000000
χ654-4-4-4444-440-40-40400000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000
χ664-4-4-4444-440-40-4040000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000
χ67888-8-8-88-8000000000000000000000000000000000000000000000000000000000000
χ688-8888-8-8-8000000000000000000000000000000000000000000000000000000000000

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