Finite Group Databasebeta

← Group #300602

Character table — Group #300602

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222444444448888888844444488888888888888888888224444444488888888224444888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
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
χ7111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111111111-1-1
χ91111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11-111-1-111-1-11-1
χ101111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-11-1-111-1-111-11
χ111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-11111-1-1-1-11-111-1-1-1-111-11
χ121111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1111111-1-1-1-1-11-1-11111-1-11-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111-1-1-11111-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1111-1-1-1-1111-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-111111-1-1-111-1-1111-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-111-1-1-1-11111-1111-1-111-1-1-11
χ17222222222-22-2-222-2222222220000-2-2-2-2-2-20000000000000000000000222200000000-2-20000000000
χ18222222222-22-2-222-2222222220000-2-2-2-2-2-20000000000000000000000-2-2-2-200000000220000000000
χ19222222222-22-2-222-2-2-2-2-2-2-2-2-20000-2-22222000000000000000000000022-2-200000000-220000000000
χ20222222222-22-2-222-2-2-2-2-2-2-2-2-20000-2-222220000000000000000000000-2-222000000002-20000000000
χ2122222222-22-222-2-22000000002222-2-200002222-2-2-2-200000000-2-222-2-2000000000000000000000000
χ2222222222-22-222-2-22000000002222-2-20000-2-2-2-2222200000000-2-2-2-222000000000000000000000000
χ2322222222-22-222-2-2200000000-2-2-2-2-2-200002222-2-2-2-20000000022-2-222000000000000000000000000
χ2422222222-22-222-2-2200000000-2-2-2-2-2-20000-2-2-2-22222000000002222-2-2000000000000000000000000
χ2522-22-2-2-220202-200-22222−2−2−2−22i2i−2i−2i0022−2−200002i2i−2i−2ii2i2i2i2−i2−i2−i2−i200002-2000022−2−2i2i2−i2−i2000000000000
χ2622-22-2-2-220202-200-22222−2−2−2−22i2i−2i−2i0022−2−20000−2i−2i2i2i−i2−i2−i2−i2i2i2i2i20000-220000−2−222i2i2−i2−i2000000000000
χ2722-22-2-2-220202-200-22222−2−2−2−2−2i−2i2i2i0022−2−200002i2i−2i−2ii2i2i2i2−i2−i2−i2−i20000-220000−2−222−i2−i2i2i2000000000000
χ2822-22-2-2-220202-200-22222−2−2−2−2−2i−2i2i2i0022−2−20000−2i−2i2i2i−i2−i2−i2−i2i2i2i2i200002-2000022−2−2−i2−i2i2i2000000000000
χ2922-22-2-2-220202-200-2−2−2−2−222222i2i−2i−2i00−2−22200002i2i−2i−2i−i2−i2−i2−i2i2i2i2i200002-20000−2−222−i2−i2i2i2000000000000
χ3022-22-2-2-220202-200-2−2−2−2−222222i2i−2i−2i00−2−2220000−2i−2i2i2ii2i2i2i2−i2−i2−i2−i20000-22000022−2−2−i2−i2i2i2000000000000
χ3122-22-2-2-220202-200-2−2−2−2−22222−2i−2i2i2i00−2−22200002i2i−2i−2i−i2−i2−i2−i2i2i2i2i20000-22000022−2−2i2i2−i2−i2000000000000
χ3222-22-2-2-220202-200-2−2−2−2−22222−2i−2i2i2i00−2−2220000−2i−2i2i2ii2i2i2i2−i2−i2−i2−i200002-20000−2−222i2i2−i2−i2000000000000
χ332-22-22-2-22020-2200-222−2−222−2−22i−2i2i−2i002−22−22i2i−2i−2i0000i2i2−i2−i2i2i2−i2−i2002-20000002−22−2i2−i2i2−i2000000000000
χ342-22-22-2-22020-2200-222−2−222−2−22i−2i2i−2i002−22−2−2i−2i2i2i0000−i2−i2i2i2−i2−i2i2i200-22000000−22−22i2−i2i2−i2000000000000
χ352-22-22-2-22020-2200-222−2−222−2−2−2i2i−2i2i002−22−22i2i−2i−2i0000i2i2−i2−i2i2i2−i2−i200-22000000−22−22−i2i2−i2i2000000000000
χ362-22-22-2-22020-2200-222−2−222−2−2−2i2i−2i2i002−22−2−2i−2i2i2i0000−i2−i2i2i2−i2−i2i2i2002-20000002−22−2−i2i2−i2i2000000000000
χ372-22-22-2-22020-2200-2−2−222−2−2222i−2i2i−2i00−22−222i2i−2i−2i0000−i2−i2i2i2−i2−i2i2i2002-2000000−22−22−i2i2−i2i2000000000000
χ382-22-22-2-22020-2200-2−2−222−2−2222i−2i2i−2i00−22−22−2i−2i2i2i0000i2i2−i2−i2i2i2−i2−i200-220000002−22−2−i2i2−i2i2000000000000
χ392-22-22-2-22020-2200-2−2−222−2−222−2i2i−2i2i00−22−222i2i−2i−2i0000−i2−i2i2i2−i2−i2i2i200-220000002−22−2i2−i2i2−i2000000000000
χ402-22-22-2-22020-2200-2−2−222−2−222−2i2i−2i2i00−22−22−2i−2i2i2i0000i2i2−i2−i2i2i2−i2−i2002-2000000−22−22i2−i2i2−i2000000000000
χ412-2-2222-2-2-20-2002202-22-22-22-200000000002−22−22−22−22−22−22−22−20000002i−2i2i−2i00000000000000i2−i2i2−i200
χ422-2-2222-2-2-20-2002202-22-22-22-200000000002−22−22−22−22−22−22−22−2000000−2i2i−2i2i00000000000000−i2i2−i2i200
χ432-2-2222-2-2-20-2002202-22-22-22-20000000000−22−22−22−22−22−22−22−220000002i−2i2i−2i00000000000000−i2i2−i2i200
χ442-2-2222-2-2-20-2002202-22-22-22-20000000000−22−22−22−22−22−22−22−22000000−2i2i−2i2i00000000000000i2−i2i2−i200
χ452-2-2222-2-2-20-200220-22-22-22-2200000000002−22−22−22−2−22−22−22−220000002i−2i−2i2i00000000000000i2−i2−i2i200
χ462-2-2222-2-2-20-200220-22-22-22-2200000000002−22−22−22−2−22−22−22−22000000−2i2i2i−2i00000000000000−i2i2i2−i200
χ472-2-2222-2-2-20-200220-22-22-22-220000000000−22−22−22−222−22−22−22−20000002i−2i−2i2i00000000000000−i2i2i2−i200
χ482-2-2222-2-2-20-200220-22-22-22-220000000000−22−22−22−222−22−22−22−2000000−2i2i2i−2i00000000000000i2−i2−i2i200
χ492-2-2-2-222222-2-2-22-22000000002-2-22-2200000000000022-2-2-2-2222-2000000002-2-220000000000000000
χ502-2-2-2-222222-2-2-22-22000000002-2-22-22000000000000-2-22222-2-22-200000000-222-20000000000000000
χ512-2-2-2-222222-2-2-22-2200000000-222-2-2200000000000022-2-2-2-222-2200000000-222-20000000000000000
χ522-2-2-2-222222-2-2-22-2200000000-222-2-22000000000000-2-22222-2-2-22000000002-2-220000000000000000
χ532-2-2-2-2222-222-2-2-22222-2-2-2-2222-2-222-22-2-220000000000000000-220000000000002-2-22000000000000
χ542-2-2-2-2222-222-2-2-22222-2-2-2-222-222-22-22-2-2200000000000000002-2000000000000-222-2000000000000
χ552-2-2-2-2222-222-2-2-222-2-22222-2-22-2-222-2-222-20000000000000000-22000000000000-222-2000000000000
χ562-2-2-2-2222-222-2-2-222-2-22222-2-2-222-22-2-222-200000000000000002-20000000000002-2-22000000000000
χ572-2-2-2-2222-2-2222-22-222-2-2-2-2220000-22-222-20000000000000000000000000000000000002-22-2000000
χ582-2-2-2-2222-2-2222-22-222-2-2-2-2220000-22-222-2000000000000000000000000000000000000-22-22000000
χ592-2-2-2-2222-2-2222-22-2-2-22222-2-20000-222-2-220000000000000000000000000000000000002-2-22000000
χ602-2-2-2-2222-2-2222-22-2-2-22222-2-20000-222-2-22000000000000000000000000000000000000-222-2000000
χ6144444444-4-4-4-4-4-4-4-40000000000004400000000000000000000000000000000000000000000000000
χ62444-4-44-4-440-400-4404-4-44-444-400000000000000000000000000000000000000000000000000000000
χ63444-4-44-4-440-400-440-444-44-4-4400000000000000000000000000000000000000000000000000000000
χ64444-4-44-4-4-404004-400000000000000000000000000022−22−2222−222222−22000000000000000000000000000000
χ65444-4-44-4-4-404004-4000000000000000000000000000−222222−2222−22−2222000000000000000000000000000000
χ6644-44-4-4-440-40-4400422222222−22−22−22−22000000−22−2222220000000000000000000000000000000000000000000000
χ6744-44-4-4-440-40-44004−22−22−22−22222222220000002222−22−220000000000000000000000000000000000000000000000
χ6844-4-44-44-40000000022−22−222222−22−222200000000002i2−2i2−2i22i200002i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
χ6944-4-44-44-40000000022−22−222222−22−22220000000000−2i22i22i2−2i20000−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ7044-4-44-44-400000000−222222−22−222222−2200000000002i2−2i2−2i22i20000−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ7144-4-44-44-400000000−222222−22−222222−220000000000−2i22i22i2−2i200002i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
χ724-444-4-44-40000000022−2222−22−2222−2222000000000000002i2−2i2−2i22i22i−2i2i−2i−2i2i−2i2i000000000000000000000000000000
χ734-444-4-44-40000000022−2222−22−2222−222200000000000000−2i22i22i2−2i2−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000
χ744-444-4-44-400000000−2222−222222−2222−22000000000000002i2−2i2−2i22i2−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000
χ754-444-4-44-400000000−2222−222222−2222−2200000000000000−2i22i22i2−2i22i−2i2i−2i−2i2i−2i2i000000000000000000000000000000
χ764-44-44-4-440-404-40042222−22−222222−22−22000000−2222−22220000000000000000000000000000000000000000000000
χ774-44-44-4-440-404-4004−22−222222−22−22222200000022−2222−220000000000000000000000000000000000000000000000
χ784-4-4444-4-440400-4-4000000000000000000022−2222−22−2222−222200000000000000000000000000000000000000
χ794-4-4444-4-440400-4-40000000000000000000−2222−222222−2222−2200000000000000000000000000000000000000
χ804-4-4-4-44444-4-4444-4-40000000000004-400000000000000000000000000000000000000000000000000

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