Finite Group Databasebeta

← Group #300563

Character table — Group #300563

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222444444448888888844444488888888888888888888444444444488888888222222888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111111111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111
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
χ71111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111
χ81111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1
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
χ111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-11111-1-1-1-11-111-1-1-1-111-11
χ121111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1111111-1-1-1-1-11-1-11111-1-11-1
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
χ151111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-111111-1-1-111-1-1111-1
χ161111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-11111-1111-1-111-1-1-11
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
χ2122222222-22-222-2-2200000000-22222-22222-2-2-2-200000000000022-2-2-2-2000000000000000000000000
χ2222222222-22-222-2-2200000000-22222-2-2-2-2-22222000000000000-2-222-2-2000000000000000000000000
χ2322222222-22-222-2-2200000000-2-2-2-2-2-22222-2-2-2-2000000000000-2-22222000000000000000000000000
χ2422222222-22-222-2-2200000000-2-2-2-2-2-2-2-2-2-2222200000000000022-2-222000000000000000000000000
χ2522-2-22-2-220-202-20022222−2−2−2−2022-2-20000022-2-222−2−22222−2−2−2−2002-200000022−2−222−2−2000000000000
χ2622-2-22-2-220-202-20022222−2−2−2−2022-2-200000-2-22222−2−2−2−2−2−2222200-22000000−2−22222−2−2000000000000
χ2722-2-22-2-220-202-20022222−2−2−2−20-2-2220000022-2-222−2−22222−2−2−2−200-22000000−2−222−2−222000000000000
χ2822-2-22-2-220-202-20022222−2−2−2−20-2-22200000-2-22222−2−2−2−2−2−22222002-200000022−2−2−2−222000000000000
χ2922-2-22-2-220-202-2002−2−2−2−22222022-2-20000022-2-2−2−222−2−2−2−22222002-2000000−2−222−2−222000000000000
χ3022-2-22-2-220-202-2002−2−2−2−22222022-2-200000-2-222−2−2222222−2−2−2−200-2200000022−2−2−2−222000000000000
χ3122-2-22-2-220-202-2002−2−2−2−222220-2-2220000022-2-2−2−222−2−2−2−2222200-2200000022−2−222−2−2000000000000
χ3222-2-22-2-220-202-2002−2−2−2−222220-2-22200000-2-222−2−2222222−2−2−2−2002-2000000−2−22222−2−2000000000000
χ332-22-2-22-220-20-2200222−2−222−2−202-22-2022-2-200002−22−222−2−222−2−22-2000000002−22−22−22−2000000000000
χ342-22-2-22-220-20-2200222−2−222−2−202-22-20-2-22200002−22−2−2−222−2−222-2200000000−22−222−22−2000000000000
χ352-22-2-22-220-20-2200222−2−222−2−20-22-22022-2-200002−22−222−2−222−2−2-2200000000−22−22−22−22000000000000
χ362-22-2-22-220-20-2200222−2−222−2−20-22-220-2-22200002−22−2−2−222−2−2222-2000000002−22−2−22−22000000000000
χ372-22-2-22-220-20-22002−2−222−2−22202-22-2022-2-20000−22−22−2−222−2−2222-200000000−22−22−22−22000000000000
χ382-22-2-22-220-20-22002−2−222−2−22202-22-20-2-2220000−22−2222−2−222−2−2-22000000002−22−2−22−22000000000000
χ392-22-2-22-220-20-22002−2−222−2−2220-22-22022-2-20000−22−22−2−222−2−222-22000000002−22−22−22−2000000000000
χ402-22-2-22-220-20-22002−2−222−2−2220-22-220-2-2220000−22−2222−2−222−2−22-200000000−22−222−22−2000000000000
χ412-2-2222-2-2-202002-202-22-22-22-2000000i2−i2i2−i2i2−i2i2−i20000i2−i2i2−i2i2−i2i2−i20000002i−2i2i−2i000000000000002−22−200
χ422-2-2222-2-2-202002-202-22-22-22-2000000i2−i2i2−i2i2−i2i2−i20000i2−i2i2−i2i2−i2i2−i2000000−2i2i−2i2i00000000000000−22−2200
χ432-2-2222-2-2-202002-202-22-22-22-2000000−i2i2−i2i2−i2i2−i2i20000−i2i2−i2i2−i2i2−i2i20000002i−2i2i−2i00000000000000−22−2200
χ442-2-2222-2-2-202002-202-22-22-22-2000000−i2i2−i2i2−i2i2−i2i20000−i2i2−i2i2−i2i2−i2i2000000−2i2i−2i2i000000000000002−22−200
χ452-2-2222-2-2-202002-20-22-22-22-22000000i2−i2i2−i2i2−i2i2−i20000−i2i2−i2i2−i2i2−i2i20000002i−2i−2i2i000000000000002−2−2200
χ462-2-2222-2-2-202002-20-22-22-22-22000000i2−i2i2−i2i2−i2i2−i20000−i2i2−i2i2−i2i2−i2i2000000−2i2i2i−2i00000000000000−222−200
χ472-2-2222-2-2-202002-20-22-22-22-22000000−i2i2−i2i2−i2i2−i2i20000i2−i2i2−i2i2−i2i2−i20000002i−2i−2i2i00000000000000−222−200
χ482-2-2222-2-2-202002-20-22-22-22-22000000−i2i2−i2i2−i2i2−i2i20000i2−i2i2−i2i2−i2i2−i2000000−2i2i2i−2i000000000000002−2−2200
χ492-2-22-2-22222-2-2-22-2200000000-22-2-22200000000000022-2-2-2-22200002-200002-2-220000000000000000
χ502-2-22-2-22222-2-2-22-2200000000-22-2-222000000000000-2-22222-2-200002-20000-222-20000000000000000
χ512-2-22-2-22222-2-2-22-2200000000-2-222-2200000000000022-2-2-2-2220000-220000-222-20000000000000000
χ522-2-22-2-22222-2-2-22-2200000000-2-222-22000000000000-2-22222-2-20000-2200002-2-220000000000000000
χ532-2-22-2-222-222-2-2-22222-2-2-2-22222-2-22-2000000002-2-22000000000000-22000000002-2-22000000000000
χ542-2-22-2-222-222-2-2-22222-2-2-2-2222-222-2-2000000002-2-220000000000002-200000000-222-2000000000000
χ552-2-22-2-222-222-2-2-222-2-22222-2-222-2-22-200000000-222-2000000000000-2200000000-222-2000000000000
χ562-2-22-2-222-222-2-2-222-2-22222-2-22-222-2-200000000-222-20000000000002-2000000002-2-22000000000000
χ572-2-22-2-222-2-2222-22-222-2-2-2-222-20000200000000-222-200000000000000000000000000002-22-2000000
χ582-2-22-2-222-2-2222-22-222-2-2-2-222-20000200000000-222-20000000000000000000000000000-22-22000000
χ592-2-22-2-222-2-2222-22-2-2-22222-2-2-200002000000002-2-2200000000000000000000000000002-2-22000000
χ602-2-22-2-222-2-2222-22-2-2-22222-2-2-200002000000002-2-220000000000000000000000000000-222-2000000
χ6144444444-4-4-4-4-4-4-4-40000000040000400000000000000000000000000000000000000000000000000
χ624444-4-4-4-440400-4-404-4-44-444-400000000000000000000000000000000000000000000000000000000
χ634444-4-4-4-440400-4-40-444-44-4-4400000000000000000000000000000000000000000000000000000000
χ644444-4-4-4-4-40-400440000000000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000
χ654444-4-4-4-4-40-40044000000000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000
χ6644-4-44-4-44040-4400-422222222−22−22−22−2200000000000000−22−22222200000000000000000000000000000000000000
χ6744-4-44-4-44040-4400-4−22−22−22−2222222222000000000000002222−22−2200000000000000000000000000000000000000
χ6844-4-4-444-40000000022−22−222222−22−22220000002i2−2i2−2i22i2000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
χ6944-4-4-444-40000000022−22−222222−22−2222000000−2i22i22i2−2i200000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ7044-4-4-444-400000000−222222−22−222222−220000002i2−2i2−2i22i200000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ7144-4-4-444-400000000−222222−22−222222−22000000−2i22i22i2−2i2000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
χ724-44-44-44-40000000022−2222−22−2222−222200000000002i2−2i2−2i22i200002i−2i2i−2i−2i2i−2i2i000000000000000000000000000000
χ734-44-44-44-40000000022−2222−22−2222−22220000000000−2i22i22i2−2i20000−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000
χ744-44-44-44-400000000−2222−222222−2222−2200000000002i2−2i2−2i22i20000−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000
χ754-44-44-44-400000000−2222−222222−2222−220000000000−2i22i22i2−2i200002i−2i2i−2i−2i2i−2i2i000000000000000000000000000000
χ764-44-4-44-440404-400-42222−22−222222−22−2200000000000000−2222−222200000000000000000000000000000000000000
χ774-44-4-44-440404-400-4−22−222222−22−2222220000000000000022−2222−2200000000000000000000000000000000000000
χ784-4-4444-4-440-400-440000000000000002i2−2i22i2−2i2−2i22i2−2i22i2000000000000000000000000000000000000000000
χ794-4-4444-4-440-400-44000000000000000−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000000000000000000000000000
χ804-4-44-4-4444-4-4444-4-40000000040000-400000000000000000000000000000000000000000000000000

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