Finite Group Databasebeta

← Group #281021

Character table — Group #281021

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222444444448888888844444488888888888888888888444444444488888888224444888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111-1-1-1-1111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ61111111111111111111111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111111111-1-1
χ91111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11-111-1-111-1-11-1
χ101111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-11-1-111-1-111-11
χ111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-111111-111-1-1-1-111-11
χ121111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-11111-11-1-11111-1-11-1
χ131111111111111111-1-1-1-1-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111-1-1-11111-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1111-1-1-1-1111-1
χ151111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-11111-1-1-1-11-1-1-111-1-1111-1
χ161111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1111111-1-1-1-1-1111-1-111-1-1-11
χ17222222222-22-2-222-222222222-20000-200000000-2-2-2-200000000000000222200000000-2-20000000000
χ18222222222-22-2-222-222222222-20000-200000000-2-2-2-200000000000000-2-2-2-200000000220000000000
χ19222222222-22-2-222-2-2-2-2-2-2-2-2-2-20000-20000000022220000000000000022-2-200000000-220000000000
χ20222222222-22-2-222-2-2-2-2-2-2-2-2-2-20000-200000000222200000000000000-2-222000000002-20000000000
χ2122222222-22-222-2-2200000000-22222-22222-2-2-2-2000000000000-2-222-2-2000000000000000000000000
χ2222222222-22-222-2-2200000000-22222-2-2-2-2-22222000000000000-2-2-2-222000000000000000000000000
χ2322222222-22-222-2-2200000000-2-2-2-2-2-22222-2-2-2-200000000000022-2-222000000000000000000000000
χ2422222222-22-222-2-2200000000-2-2-2-2-2-2-2-2-2-222220000000000002222-2-2000000000000000000000000
χ2522-22-22-2-20-202-20022222−2−2−2−202i2i−2i−2i022-2-2000022−2−22222−2−2−2−2002i−2i000000i2i2−i2−i2i2i2−i2−i2000000000000
χ2622-22-22-2-20-202-20022222−2−2−2−202i2i−2i−2i0-2-222000022−2−2−2−2−2−2222200−2i2i000000i2i2−i2−i2−i2−i2i2i2000000000000
χ2722-22-22-2-20-202-20022222−2−2−2−20−2i−2i2i2i022-2-2000022−2−22222−2−2−2−200−2i2i000000−i2−i2i2i2−i2−i2i2i2000000000000
χ2822-22-22-2-20-202-20022222−2−2−2−20−2i−2i2i2i0-2-222000022−2−2−2−2−2−22222002i−2i000000−i2−i2i2i2i2i2−i2−i2000000000000
χ2922-22-22-2-20-202-2002−2−2−2−2222202i2i−2i−2i022-2-20000−2−222−2−2−2−22222002i−2i000000−i2−i2i2i2−i2−i2i2i2000000000000
χ3022-22-22-2-20-202-2002−2−2−2−2222202i2i−2i−2i0-2-2220000−2−2222222−2−2−2−200−2i2i000000−i2−i2i2i2i2i2−i2−i2000000000000
χ3122-22-22-2-20-202-2002−2−2−2−222220−2i−2i2i2i022-2-20000−2−222−2−2−2−2222200−2i2i000000i2i2−i2−i2i2i2−i2−i2000000000000
χ3222-22-22-2-20-202-2002−2−2−2−222220−2i−2i2i2i0-2-2220000−2−2222222−2−2−2−2002i−2i000000i2i2−i2−i2−i2−i2i2i2000000000000
χ332-222-2-2-22-202002-2022-2-222-2-2000000i2−i2i2−i2i2i2−i2−i20000i2i2−i2−i2i2i2−i2−i20000002i−2i2i−2i000000000000002−22−200
χ342-222-2-2-22-202002-2022-2-222-2-2000000i2−i2i2−i2i2i2−i2−i20000i2i2−i2−i2i2i2−i2−i2000000−2i2i−2i2i00000000000000−22−2200
χ352-222-2-2-22-202002-2022-2-222-2-2000000−i2i2−i2i2−i2−i2i2i20000−i2−i2i2i2−i2−i2i2i20000002i−2i2i−2i00000000000000−22−2200
χ362-222-2-2-22-202002-2022-2-222-2-2000000−i2i2−i2i2−i2−i2i2i20000−i2−i2i2i2−i2−i2i2i2000000−2i2i−2i2i000000000000002−22−200
χ372-222-2-2-22-202002-20-2-222-2-222000000i2−i2i2−i2i2i2−i2−i20000−i2−i2i2i2−i2−i2i2i20000002i−2i−2i2i000000000000002−2−2200
χ382-222-2-2-22-202002-20-2-222-2-222000000i2−i2i2−i2i2i2−i2−i20000−i2−i2i2i2−i2−i2i2i2000000−2i2i2i−2i00000000000000−222−200
χ392-222-2-2-22-202002-20-2-222-2-222000000−i2i2−i2i2−i2−i2i2i20000i2i2−i2−i2i2i2−i2−i20000002i−2i−2i2i00000000000000−222−200
χ402-222-2-2-22-202002-20-2-222-2-222000000−i2i2−i2i2−i2−i2i2i20000i2i2−i2−i2i2i2−i2−i2000000−2i2i2i−2i000000000000002−2−2200
χ412-22-222-2-222-2-2-22-2200000000-22i−2i2i−2i20000000000002-22-22-22-22i−2i0000000000002i−2i2i−2i000000000000
χ422-22-222-2-222-2-2-22-2200000000-22i−2i2i−2i2000000000000-22-22-22-222i−2i000000000000−2i2i−2i2i000000000000
χ432-22-222-2-222-2-2-22-2200000000-2−2i2i−2i2i20000000000002-22-22-22-2−2i2i000000000000−2i2i−2i2i000000000000
χ442-22-222-2-222-2-2-22-2200000000-2−2i2i−2i2i2000000000000-22-22-22-22−2i2i0000000000002i−2i2i−2i000000000000
χ452-22-222-2-2-222-2-2-2222-22-22-22-222i−2i2i−2i-2000000002-22-200000000−2i2i000000002i−2i2i−2i0000000000000000
χ462-22-222-2-2-222-2-2-2222-22-22-22-22−2i2i−2i2i-2000000002-22-2000000002i−2i00000000−2i2i−2i2i0000000000000000
χ472-22-222-2-2-222-2-2-222-22-22-22-2222i−2i2i−2i-200000000-22-2200000000−2i2i00000000−2i2i−2i2i0000000000000000
χ482-22-222-2-2-222-2-2-222-22-22-22-222−2i2i−2i2i-200000000-22-22000000002i−2i000000002i−2i2i−2i0000000000000000
χ492-22-222-2-2-2-2222-22-22-22-22-22-2-20000200000000-22-2200000000000000000000000000002i−2i2i−2i000000
χ502-22-222-2-2-2-2222-22-22-22-22-22-2-20000200000000-22-220000000000000000000000000000−2i2i−2i2i000000
χ512-22-222-2-2-2-2222-22-2-22-22-22-22-200002000000002-22-200000000000000000000000000002i−2i−2i2i000000
χ522-22-222-2-2-2-2222-22-2-22-22-22-22-200002000000002-22-20000000000000000000000000000−2i2i2i−2i000000
χ532-2-2-2-22220-20-220022−22−2−22−2202-2-22000002-22-22−2−222−22−2−22−2200002-200002−2−222−2−22000000000000
χ542-2-2-2-22220-20-220022−22−2−22−2202-2-2200000-22-222−2−22−22−222−22−20000-2200002−2−22−222−2000000000000
χ552-2-2-2-22220-20-220022−22−2−22−220-222-2000002-22-22−2−222−22−2−22−220000-220000−222−2−222−2000000000000
χ562-2-2-2-22220-20-220022−22−2−22−220-222-200000-22-222−2−22−22−222−22−200002-20000−222−22−2−22000000000000
χ572-2-2-2-22220-20-22002−22−222−22−202-2-22000002-22-2−222−2−22−222−22−200002-20000−222−2−222−2000000000000
χ582-2-2-2-22220-20-22002−22−222−22−202-2-2200000-22-22−222−22−22−2−22−220000-220000−222−22−2−22000000000000
χ592-2-2-2-22220-20-22002−22−222−22−20-222-2000002-22-2−222−2−22−222−22−20000-2200002−2−222−2−22000000000000
χ602-2-2-2-22220-20-22002−22−222−22−20-222-200000-22-22−222−22−22−2−22−2200002-200002−2−22−222−2000000000000
χ6144444444-4-4-4-4-4-4-4-40000000040000400000000000000000000000000000000000000000000000000
χ62444-4-4-44-440400-4-404-4-444-4-4400000000000000000000000000000000000000000000000000000000
χ63444-4-4-44-440400-4-40-444-4-444-400000000000000000000000000000000000000000000000000000000
χ64444-4-4-44-4-40-400440000000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000
χ65444-4-4-44-4-40-40044000000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000
χ6644-44-44-4-4040-4400-422222222−22−22−22−2200000000000000−22−22222200000000000000000000000000000000000000
χ6744-44-44-4-4040-4400-4−22−22−22−2222222222000000000000002222−22−2200000000000000000000000000000000000000
χ6844-4-44-4-440000000022−22−2222−222222−2200000000002i2−2i2−2i22i200002i−2i−2i2i−2i2i2i−2i000000000000000000000000000000
χ6944-4-44-4-440000000022−22−2222−222222−220000000000−2i22i22i2−2i20000−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000
χ7044-4-44-4-4400000000−222222−2222−22−222200000000002i2−2i2−2i22i20000−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000
χ7144-4-44-4-4400000000−222222−2222−22−22220000000000−2i22i22i2−2i200002i−2i−2i2i−2i2i2i−2i000000000000000000000000000000
χ724-444-4-4-4440-400-440000000000000002i2−2i22i2−2i2−2i2−2i22i22i2000000000000000000000000000000000000000000
χ734-444-4-4-4440-400-44000000000000000−2i22i2−2i22i22i22i2−2i2−2i2000000000000000000000000000000000000000000
χ744-44-444-4-44-4-4444-4-40000000040000-400000000000000000000000000000000000000000000000000
χ754-4-444-44-4000000002222−22−22−22−2222220000002i2−2i2−2i22i2000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ764-4-444-44-4000000002222−22−22−22−222222000000−2i22i22i2−2i200000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ774-4-444-44-400000000−22−2222222222−22−220000002i2−2i2−2i22i200000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ784-4-444-44-400000000−22−2222222222−22−22000000−2i22i22i2−2i2000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ794-4-4-4-44440404-400-422−2222−22−2222−222200000000000000−222222−2200000000000000000000000000000000000000
χ804-4-4-4-44440404-400-4−2222−222222−2222−220000000000000022−22−222200000000000000000000000000000000000000

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