Finite Group Databasebeta

← Group #312928

Character table — Group #312928

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444444444448888888844444444448888888888888888224444888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111111-1-1-11
χ61111111111111111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111-1-1-1-1-1111-1
χ71111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1111-1-1111-1
χ81111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111111-1-1-111-1-1-11
χ911111111111111111-1-1-1-1111111111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11-1-11-1-1-1-111
χ1011111111111111111-1-1-1-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-111-11111-1-1
χ1111111111111111111-1-1-1-1111111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-11-1-111111-1-1
χ1211111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111-111-1-1-1-1-111
χ1311111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1111111-1-1-11-1-111-11
χ1411111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-11111-1-1111-111-1-11-1
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-111-1-1-1111-1-11-1
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1111-1-1-111-11
χ17222222222-22-22-22-2-22222-200000000-2-222-2-20000220000-2-200000000000000000000
χ18222222222-22-22-22-2-22222-200000000-2-2-2-2220000-2-200002200000000000000000000
χ19222222222-22-22-22-2-2-2-2-2-2-2000000002222-2-20000-2-200002200000000000000000000
χ20222222222-22-22-22-2-2-2-2-2-2-20000000022-2-2220000220000-2-200000000000000000000
χ2122222222-22-22-22-22-20000-22222-2-2-2-200000022-2-2000000000000000000200-2000000
χ2222222222-22-22-22-22-20000-22222-2-2-2-2000000-2-222000000000000000000-2002000000
χ2322222222-22-22-22-22-20000-2-2-2-2-222220000002222000000000000000000-200-2000000
χ2422222222-22-22-22-22-20000-2-2-2-2-22222000000-2-2-2-20000000000000000002002000000
χ2522-222-2-2-2-20-20202002i2i−2i−2i022−2−222−2−2002-20000002i−2ii2i2−i2−i20022−2−2i2i2−i2−i2000000000000
χ2622-222-2-2-2-20-20202002i2i−2i−2i022−2−222−2−200-22000000−2i2ii2i2−i2−i200−2−222−i2−i2i2i2000000000000
χ2722-222-2-2-2-20-20202002i2i−2i−2i0−2−222−2−222002-20000002i−2i−i2−i2i2i200−2−222−i2−i2i2i2000000000000
χ2822-222-2-2-2-20-20202002i2i−2i−2i0−2−222−2−22200-22000000−2i2i−i2−i2i2i20022−2−2i2i2−i2−i2000000000000
χ2922-222-2-2-2-20-2020200−2i−2i2i2i022−2−222−2−2002-2000000−2i2i−i2−i2i2i20022−2−2−i2−i2i2i2000000000000
χ3022-222-2-2-2-20-2020200−2i−2i2i2i022−2−222−2−200-220000002i−2i−i2−i2i2i200−2−222i2i2−i2−i2000000000000
χ3122-222-2-2-2-20-2020200−2i−2i2i2i0−2−222−2−222002-2000000−2i2ii2i2−i2−i200−2−222i2i2−i2−i2000000000000
χ3222-222-2-2-2-20-2020200−2i−2i2i2i0−2−222−2−22200-220000002i−2ii2i2−i2−i20022−2−2−i2−i2i2i2000000000000
χ332-222-2-2-22-202020-2002-22-20i2−i2i2−i2i2−i2i2−i200002i−2i000000i2−i2i2−i22i−2i2−22−22−22−2000000000000
χ342-222-2-2-22-202020-2002-22-20i2−i2i2−i2i2−i2i2−i20000−2i2i000000i2−i2i2−i2−2i2i−22−22−22−22000000000000
χ352-222-2-2-22-202020-2002-22-20−i2i2−i2i2−i2i2−i2i200002i−2i000000−i2i2−i2i22i−2i−22−22−22−22000000000000
χ362-222-2-2-22-202020-2002-22-20−i2i2−i2i2−i2i2−i2i20000−2i2i000000−i2i2−i2i2−2i2i2−22−22−22−2000000000000
χ372-222-2-2-22-202020-200-22-220i2−i2i2−i2i2−i2i2−i200002i−2i000000−i2i2−i2i2−2i2i2−22−2−22−22000000000000
χ382-222-2-2-22-202020-200-22-220i2−i2i2−i2i2−i2i2−i20000−2i2i000000−i2i2−i2i22i−2i−22−222−22−2000000000000
χ392-222-2-2-22-202020-200-22-220−i2i2−i2i2−i2i2−i2i200002i−2i000000i2−i2i2−i2−2i2i−22−222−22−2000000000000
χ402-222-2-2-22-202020-200-22-220−i2i2−i2i2−i2i2−i2i20000−2i2i000000i2−i2i2−i22i−2i2−22−2−22−22000000000000
χ412-2-22-222-222-2-222-2-2-22i−2i−2i2i22i−2i−2i2i2i−2i−2i2i2i−2i0000000000-222-20000000000000000000000
χ422-2-22-222-222-2-222-2-2-22i−2i−2i2i2−2i2i2i−2i−2i2i2i−2i2i−2i00000000002-2-220000000000000000000000
χ432-2-22-222-222-2-222-2-2-2−2i2i2i−2i22i−2i−2i2i2i−2i−2i2i−2i2i00000000002-2-220000000000000000000000
χ442-2-22-222-222-2-222-2-2-2−2i2i2i−2i2−2i2i2i−2i−2i2i2i−2i−2i2i0000000000-222-20000000000000000000000
χ452-2-22-222-22-2-222-2-2222i−2i−2i2i-200000000−2i2i00000000000000002-2-222i−2i−2i2i000000000000
χ462-2-22-222-22-2-222-2-2222i−2i−2i2i-200000000−2i2i0000000000000000-222-2−2i2i2i−2i000000000000
χ472-2-22-222-22-2-222-2-222−2i2i2i−2i-2000000002i−2i00000000000000002-2-22−2i2i2i−2i000000000000
χ482-2-22-222-22-2-222-2-222−2i2i2i−2i-2000000002i−2i0000000000000000-222-22i−2i−2i2i000000000000
χ492-2-22-222-2-222-2-222-220000-22i−2i−2i2i−2i2i2i−2i000000000000000000000000002-202i−2i0000000
χ502-2-22-222-2-222-2-222-220000-22i−2i−2i2i−2i2i2i−2i00000000000000000000000000-220−2i2i0000000
χ512-2-22-222-2-222-2-222-220000-2−2i2i2i−2i2i−2i−2i2i000000000000000000000000002-20−2i2i0000000
χ522-2-22-222-2-222-2-222-220000-2−2i2i2i−2i2i−2i−2i2i00000000000000000000000000-2202i−2i0000000
χ5344444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000000
χ5444-444-4-4-44040-40-400000002222−22−22−22−22222200000000000000000000000000000000000000
χ5544-444-4-4-44040-40-40000000−22−2222222222−22−2200000000000000000000000000000000000000
χ5644-4-4-4-44404040-40-4000000000000000000004i−4i000000000000000000000000000000
χ5744-4-4-4-44404040-40-400000000000000000000−4i4i000000000000000000000000000000
χ5844-4-4-4-4440-40-40404000000000000000000000000000000000000000000000022−220000
χ5944-4-4-4-4440-40-404040000000000000000000000000000000000000000000000−22220000
χ604-444-4-4-4440-40-40400000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000000000
χ614-444-4-4-4440-40-4040000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000000000
χ624-44-44-44-4040-40-40400000000000000000000004i−4i0000000000000000000000000000
χ634-44-44-44-4040-40-4040000000000000000000000−4i4i0000000000000000000000000000
χ644-44-44-44-40-404040-40000000000000000000000000000000000000000000000002i2−2i200
χ654-44-44-44-40-404040-4000000000000000000000000000000000000000000000000−2i22i200
χ664-4-44-444-4-4-444-4-444-4000040000000000000000000000000000000000000000000000
χ67888-8-88-8-8000000000000000000000000000000000000000000000000000000000000
χ688-8-8-888-88000000000000000000000000000000000000000000000000000000000000

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