Finite Group Databasebeta

← Group #300567

Character table — Group #300567

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222444444448888888844444488888888888888888888444444444488888888222222888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
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
χ4111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ6111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1
χ91111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-11-111-1-111-1-11-1
χ101111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-11-1-111-1-111-11
χ111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1111111-1-1-1-11-111-1-1-1-111-11
χ121111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-11-1-11111-1-11-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111-1-1-11111-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1111-1-1-1-1111-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111111-1-1-111-1-1111-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-11111-1111-1-111-1-1-11
χ17222222222-22-2-222-2222222220000-2-200000000-2-2-2-200000000000022220000000000-2-20000000000
χ18222222222-22-2-222-2222222220000-2-200000000-2-2-2-2000000000000-2-2-2-20000000000220000000000
χ19222222222-22-2-222-2-2-2-2-2-2-2-2-20000-2-200000000222200000000000022-2-20000000000-220000000000
χ20222222222-22-2-222-2-2-2-2-2-2-2-2-20000-2-2000000002222000000000000-2-22200000000002-20000000000
χ2122222222-22-222-2-22000000002222-2-22222-2-2-2-200000000000022-2-20000-2-200000000000000000000
χ2222222222-22-222-2-22000000002222-2-2-2-2-2-22222000000000000-2-2220000-2-200000000000000000000
χ2322222222-22-222-2-2200000000-2-2-2-2-2-22222-2-2-2-2000000000000-2-22200002200000000000000000000
χ2422222222-22-222-2-2200000000-2-2-2-2-2-2-2-2-2-2222200000000000022-2-200002200000000000000000000
χ2522-2-22-22-20202-200-22222−2−2−2−222-2-20000002i2i−2i−2i22−2−2i2i2i2i2−i2−i2−i2−i2002i−2i000000i2i2−i2−i222−2−2000000000000
χ2622-2-22-22-20202-200-22222−2−2−2−222-2-2000000−2i−2i2i2i22−2−2−i2−i2−i2−i2i2i2i2i200−2i2i000000−i2−i2i2i222−2−2000000000000
χ2722-2-22-22-20202-200-22222−2−2−2−2-2-2220000002i2i−2i−2i22−2−2i2i2i2i2−i2−i2−i2−i200−2i2i000000−i2−i2i2i2−2−222000000000000
χ2822-2-22-22-20202-200-22222−2−2−2−2-2-222000000−2i−2i2i2i22−2−2−i2−i2−i2−i2i2i2i2i2002i−2i000000i2i2−i2−i2−2−222000000000000
χ2922-2-22-22-20202-200-2−2−2−2−2222222-2-20000002i2i−2i−2i−2−222−i2−i2−i2−i2i2i2i2i2002i−2i000000−i2−i2i2i2−2−222000000000000
χ3022-2-22-22-20202-200-2−2−2−2−2222222-2-2000000−2i−2i2i2i−2−222i2i2i2i2−i2−i2−i2−i200−2i2i000000i2i2−i2−i2−2−222000000000000
χ3122-2-22-22-20202-200-2−2−2−2−22222-2-2220000002i2i−2i−2i−2−222−i2−i2−i2−i2i2i2i2i200−2i2i000000i2i2−i2−i222−2−2000000000000
χ3222-2-22-22-20202-200-2−2−2−2−22222-2-222000000−2i−2i2i2i−2−222i2i2i2i2−i2−i2−i2−i2002i−2i000000−i2−i2i2i222−2−2000000000000
χ332-22-2-222-2020-2200-222−2−222−2−22-22-2002i2i−2i−2i00002−22−2i2i2−i2−i2i2i2−i2−i22i−2i00000000i2−i2i2−i22−22−2000000000000
χ342-22-2-222-2020-2200-222−2−222−2−22-22-200−2i−2i2i2i00002−22−2−i2−i2i2i2−i2−i2i2i2−2i2i00000000−i2i2−i2i22−22−2000000000000
χ352-22-2-222-2020-2200-222−2−222−2−2-22-22002i2i−2i−2i00002−22−2i2i2−i2−i2i2i2−i2−i2−2i2i00000000−i2i2−i2i2−22−22000000000000
χ362-22-2-222-2020-2200-222−2−222−2−2-22-2200−2i−2i2i2i00002−22−2−i2−i2i2i2−i2−i2i2i22i−2i00000000i2−i2i2−i2−22−22000000000000
χ372-22-2-222-2020-2200-2−2−222−2−2222-22-2002i2i−2i−2i0000−22−22−i2−i2i2i2−i2−i2i2i22i−2i00000000−i2i2−i2i2−22−22000000000000
χ382-22-2-222-2020-2200-2−2−222−2−2222-22-200−2i−2i2i2i0000−22−22i2i2−i2−i2i2i2−i2−i2−2i2i00000000i2−i2i2−i2−22−22000000000000
χ392-22-2-222-2020-2200-2−2−222−2−222-22-22002i2i−2i−2i0000−22−22−i2−i2i2i2−i2−i2i2i2−2i2i00000000i2−i2i2−i22−22−2000000000000
χ402-22-2-222-2020-2200-2−2−222−2−222-22-2200−2i−2i2i2i0000−22−22i2i2−i2−i2i2i2−i2−i22i−2i00000000−i2i2−i2i22−22−2000000000000
χ412-2-2222-2-2-202002-202-22-22-22-2000000i2−i2i2−i2i2−i2i2−i20000i2−i2i2−i2i2−i2i2−i200002i−2i2i−2i00000000000000002−22−200
χ422-2-2222-2-2-202002-202-22-22-22-2000000i2−i2i2−i2i2−i2i2−i20000i2−i2i2−i2i2−i2i2−i20000−2i2i−2i2i0000000000000000−22−2200
χ432-2-2222-2-2-202002-202-22-22-22-2000000−i2i2−i2i2−i2i2−i2i20000−i2i2−i2i2−i2i2−i2i200002i−2i2i−2i0000000000000000−22−2200
χ442-2-2222-2-2-202002-202-22-22-22-2000000−i2i2−i2i2−i2i2−i2i20000−i2i2−i2i2−i2i2−i2i20000−2i2i−2i2i00000000000000002−22−200
χ452-2-2222-2-2-202002-20-22-22-22-22000000i2−i2i2−i2i2−i2i2−i20000−i2i2−i2i2−i2i2−i2i200002i−2i−2i2i00000000000000002−2−2200
χ462-2-2222-2-2-202002-20-22-22-22-22000000i2−i2i2−i2i2−i2i2−i20000−i2i2−i2i2−i2i2−i2i20000−2i2i2i−2i0000000000000000−222−200
χ472-2-2222-2-2-202002-20-22-22-22-22000000−i2i2−i2i2−i2i2−i2i20000i2−i2i2−i2i2−i2i2−i200002i−2i−2i2i0000000000000000−222−200
χ482-2-2222-2-2-202002-20-22-22-22-22000000−i2i2−i2i2−i2i2−i2i20000i2−i2i2−i2i2−i2i2−i20000−2i2i2i−2i00000000000000002−2−2200
χ492-2-22-2-22222-2-2-22-22000000002-2-22-2200000000000022-2-2-2-222000000002-22-2-220000000000000000
χ502-2-22-2-22222-2-2-22-22000000002-2-22-22000000000000-2-22222-2-2000000002-2-222-20000000000000000
χ512-2-22-2-22222-2-2-22-2200000000-222-2-2200000000000022-2-2-2-22200000000-22-222-20000000000000000
χ522-2-22-2-22222-2-2-22-2200000000-222-2-22000000000000-2-22222-2-200000000-222-2-220000000000000000
χ532-2-22-2-222-222-2-2-22222-2-2-2-2222-2-222-2000000002-2-220000000000000000-2200002-2-22000000000000
χ542-2-22-2-222-222-2-2-22222-2-2-2-222-222-22-2000000002-2-2200000000000000002-20000-222-2000000000000
χ552-2-22-2-222-222-2-2-222-2-22222-2-22-2-222-200000000-222-20000000000000000-220000-222-2000000000000
χ562-2-22-2-222-222-2-2-222-2-22222-2-2-222-22-200000000-222-200000000000000002-200002-2-22000000000000
χ572-2-22-2-222-2-2222-22-222-2-2-2-2220000-2200000000-222-200000000000000000000000000002-22-2000000
χ582-2-22-2-222-2-2222-22-222-2-2-2-2220000-2200000000-222-20000000000000000000000000000-22-22000000
χ592-2-22-2-222-2-2222-22-2-2-22222-2-20000-22000000002-2-2200000000000000000000000000002-2-22000000
χ602-2-22-2-222-2-2222-22-2-2-22222-2-20000-22000000002-2-220000000000000000000000000000-222-2000000
χ6144444444-4-4-4-4-4-4-4-40000000000004400000000000000000000000000000000000000000000000000
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
χ6644-4-44-44-40-40-4400422222222−22−22−22−2200000000000000−22−22222200000000000000000000000000000000000000
χ6744-4-44-44-40-40-44004−22−22−22−2222222222000000000000002222−22−2200000000000000000000000000000000000000
χ6844-4-4-44-440000000022−22−222222−22−222200000022−22−2222000000002-2-222-2-22000000000000000000000000000000
χ6944-4-4-44-440000000022−22−222222−22−2222000000−222222−2200000000-222-2-222-2000000000000000000000000000000
χ7044-4-4-44-4400000000−222222−22−222222−2200000022−22−222200000000-222-2-222-2000000000000000000000000000000
χ7144-4-4-44-4400000000−222222−22−222222−22000000−222222−22000000002-2-222-2-22000000000000000000000000000000
χ724-44-44-4-440000000022−2222−22−2222−2222000000000022−22−222200002-22-2-22-22000000000000000000000000000000
χ734-44-44-4-440000000022−2222−22−2222−22220000000000−222222−220000-22-222-22-2000000000000000000000000000000
χ744-44-44-4-4400000000−2222−222222−2222−22000000000022−22−22220000-22-222-22-2000000000000000000000000000000
χ754-44-44-4-4400000000−2222−222222−2222−220000000000−222222−2200002-22-2-22-22000000000000000000000000000000
χ764-44-4-444-40-404-40042222−22−222222−22−2200000000000000−2222−222200000000000000000000000000000000000000
χ774-44-4-444-40-404-4004−22−222222−22−2222220000000000000022−2222−2200000000000000000000000000000000000000
χ784-4-4444-4-440-400-440000000000000002i2−2i22i2−2i2−2i22i2−2i22i2000000000000000000000000000000000000000000
χ794-4-4444-4-440-400-44000000000000000−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000000000000000000000000000
χ804-4-44-4-4444-4-4444-4-40000000000004-400000000000000000000000000000000000000000000000000

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