Finite Group Databasebeta

← Group #351535

Character table — Group #351535

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11111111222222224444444444444444444444444444444444444444444444444444444444161616161616161632323232
order12222222444444442244444444444444444444444488888888888888888888888888888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ51111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1111111-1-1
χ91111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11-11-1
χ101111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-11-11
χ111111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1111-1-11
χ121111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-111-1
χ131111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-11-11
χ141111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111-11-1
χ151111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-111-1
χ161111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-11-1-11
χ1722222222222-2-2-2-2222-2-2-2-20000000022-2-2000000002222-2-2-2-22222-2-2-2-20000000000000000000000000000
χ1822222222222-2-2-2-2222-2-2-2-20000000022-2-200000000-2-2-2-22222-2-2-2-222220000000000000000000000000000
χ1922222222222-2-2-2-22-2-2-2-22200000000-2-222000000002222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ2022222222222-2-2-2-22-2-2-2-22200000000-2-22200000000-2-2-2-222222222-2-2-2-20000000000000000000000000000
χ2122222222-2-2-22222-222-2-2-2-22222-2-2-2-2-2-2222222-2-2-2-200000000000000000000000000000000000000000000
χ2222222222-2-2-22222-222-2-2-2-2-2-2-2-22222-2-222-2-2-2-2222200000000000000000000000000000000000000000000
χ2322222222-2-2-22222-2-2-2-2-2222222-2-2-2-222-2-2-2-2-2-2222200000000000000000000000000000000000000000000
χ2422222222-2-2-22222-2-2-2-2-222-2-2-2-2222222-2-22222-2-2-2-200000000000000000000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-222222200000000-2-2-2-20000000000000000000000002i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i000000000000
χ2622222222-2-2-2-2-2-2-2-222222200000000-2-2-2-2000000000000000000000000−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-222-2-20000000022220000000000000000000000002i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-222-2-2000000002222000000000000000000000000−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i000000000000
χ2922-2-222-2-200022-2-2000002i−2i00002i2i−2i−2i2i−2i0022-2-20000i2i2−i2−i2i2i2−i2−i222−2−222−2−222−2−222−2−2i2i2−i2−i2i2i2−i2−i2000000000000
χ3022-2-222-2-200022-2-2000002i−2i00002i2i−2i−2i2i−2i0022-2-20000−i2−i2i2i2−i2−i2i2i2−2−222−2−222−2−222−2−222−i2−i2i2i2−i2−i2i2i2000000000000
χ3122-2-222-2-200022-2-2000002i−2i0000−2i−2i2i2i2i−2i00-2-2220000i2i2−i2−i2i2i2−i2−i222−2−222−2−2−2−222−2−222−i2−i2i2i2−i2−i2i2i2000000000000
χ3222-2-222-2-200022-2-2000002i−2i0000−2i−2i2i2i2i−2i00-2-2220000−i2−i2i2i2−i2−i2i2i2−2−222−2−22222−2−222−2−2i2i2−i2−i2i2i2−i2−i2000000000000
χ3322-2-222-2-200022-2-200000−2i2i00002i2i−2i−2i−2i2i00-2-2220000i2i2−i2−i2i2i2−i2−i2−2−222−2−22222−2−222−2−2−i2−i2i2i2−i2−i2i2i2000000000000
χ3422-2-222-2-200022-2-200000−2i2i00002i2i−2i−2i−2i2i00-2-2220000−i2−i2i2i2−i2−i2i2i222−2−222−2−2−2−222−2−222i2i2−i2−i2i2i2−i2−i2000000000000
χ3522-2-222-2-200022-2-200000−2i2i0000−2i−2i2i2i−2i2i0022-2-20000i2i2−i2−i2i2i2−i2−i2−2−222−2−222−2−222−2−222i2i2−i2−i2i2i2−i2−i2000000000000
χ3622-2-222-2-200022-2-200000−2i2i0000−2i−2i2i2i−2i2i0022-2-20000−i2−i2i2i2−i2−i2i2i222−2−222−2−222−2−222−2−2−i2−i2i2i2−i2−i2i2i2000000000000
χ3722-2-222-2-2000-2-222000002i−2i22-2-20000−2i2i0000002i2i−2i−2ii2i2−i2−i2−i2−i2i2i2−2−22222−2−2i2i2−i2−i2−i2−i2i2i2−2−22222−2−2000000000000
χ3822-2-222-2-2000-2-222000002i−2i22-2-20000−2i2i0000002i2i−2i−2i−i2−i2i2i2i2i2−i2−i222−2−2−2−222−i2−i2i2i2i2i2−i2−i222−2−2−2−222000000000000
χ3922-2-222-2-2000-2-222000002i−2i-2-2220000−2i2i000000−2i−2i2i2ii2i2−i2−i2−i2−i2i2i2−2−22222−2−2−i2−i2i2i2i2i2−i2−i222−2−2−2−222000000000000
χ4022-2-222-2-2000-2-222000002i−2i-2-2220000−2i2i000000−2i−2i2i2i−i2−i2i2i2i2i2−i2−i222−2−2−2−222i2i2−i2−i2−i2−i2i2i2−2−22222−2−2000000000000
χ4122-2-222-2-2000-2-22200000−2i2i22-2-200002i−2i000000−2i−2i2i2ii2i2−i2−i2−i2−i2i2i222−2−2−2−222i2i2−i2−i2−i2−i2i2i222−2−2−2−222000000000000
χ4222-2-222-2-2000-2-22200000−2i2i22-2-200002i−2i000000−2i−2i2i2i−i2−i2i2i2i2i2−i2−i2−2−22222−2−2−i2−i2i2i2i2i2−i2−i2−2−22222−2−2000000000000
χ4322-2-222-2-2000-2-22200000−2i2i-2-22200002i−2i0000002i2i−2i−2ii2i2−i2−i2−i2−i2i2i222−2−2−2−222−i2−i2i2i2i2i2−i2−i2−2−22222−2−2000000000000
χ4422-2-222-2-2000-2-22200000−2i2i-2-22200002i−2i0000002i2i−2i−2i−i2−i2i2i2i2i2−i2−i2−2−22222−2−2i2i2−i2−i2−i2−i2i2i222−2−2−2−222000000000000
χ452-22-22-22-20002-22-202-2000000002-22-2002-200002-22-2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000
χ462-22-22-22-20002-22-202-2000000002-22-2002-200002-22-2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000
χ472-22-22-22-20002-22-202-200000000-22-22002-20000-22-22i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000
χ482-22-22-22-20002-22-202-200000000-22-22002-20000-22-22−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000
χ492-22-22-22-20002-22-20-22000000002-22-200-220000-22-22i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000000000
χ502-22-22-22-20002-22-20-22000000002-22-200-220000-22-22−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000000000
χ512-22-22-22-20002-22-20-2200000000-22-2200-2200002-22-2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000000000
χ522-22-22-22-20002-22-20-2200000000-22-2200-2200002-22-2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000000000
χ532-22-22-22-2000-22-2202-200002i−2i2i−2i000000-222i−2i2i−2i0000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i22−22−2−22−222−22−2−22−22000000000000
χ542-22-22-22-2000-22-2202-200002i−2i2i−2i000000-222i−2i2i−2i0000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−22−222−22−2−22−222−22−2000000000000
χ552-22-22-22-2000-22-2202-20000−2i2i−2i2i000000-22−2i2i−2i2i0000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2−22−222−22−2−22−222−22−2000000000000
χ562-22-22-22-2000-22-2202-20000−2i2i−2i2i000000-22−2i2i−2i2i0000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i22−22−2−22−222−22−2−22−22000000000000
χ572-22-22-22-2000-22-220-2200002i−2i2i−2i0000002-2−2i2i−2i2i0000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i22−22−2−22−22−22−222−22−2000000000000
χ582-22-22-22-2000-22-220-2200002i−2i2i−2i0000002-2−2i2i−2i2i0000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−22−222−22−22−22−2−22−22000000000000
χ592-22-22-22-2000-22-220-220000−2i2i−2i2i0000002-22i−2i2i−2i0000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2−22−222−22−22−22−2−22−22000000000000
χ602-22-22-22-2000-22-220-220000−2i2i−2i2i0000002-22i−2i2i−2i0000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i22−22−2−22−22−22−222−22−2000000000000
χ612-2-222-2-222-2-22-2-222002-2002i−2i−2i2i−2i2i2i−2i000000000000000000002i−2i−2i2i2i−2i−2i2i000000002-2-222-2-22000000000000
χ622-2-222-2-222-2-22-2-222002-2002i−2i−2i2i−2i2i2i−2i00000000000000000000−2i2i2i−2i−2i2i2i−2i00000000-222-2-222-2000000000000
χ632-2-222-2-222-2-22-2-222002-200−2i2i2i−2i2i−2i−2i2i000000000000000000002i−2i−2i2i2i−2i−2i2i00000000-222-2-222-2000000000000
χ642-2-222-2-222-2-22-2-222002-200−2i2i2i−2i2i−2i−2i2i00000000000000000000−2i2i2i−2i−2i2i2i−2i000000002-2-222-2-22000000000000
χ652-2-222-2-222-2-2-222-2200-22000000000000002i−2i−2i2i2i−2i−2i2i000000002i−2i−2i2i−2i2i2i−2i2-2-22-222-200000000000000000000
χ662-2-222-2-222-2-2-222-2200-22000000000000002i−2i−2i2i2i−2i−2i2i00000000−2i2i2i−2i2i−2i−2i2i-222-22-2-2200000000000000000000
χ672-2-222-2-222-2-2-222-2200-2200000000000000−2i2i2i−2i−2i2i2i−2i000000002i−2i−2i2i−2i2i2i−2i-222-22-2-2200000000000000000000
χ682-2-222-2-222-2-2-222-2200-2200000000000000−2i2i2i−2i−2i2i2i−2i00000000−2i2i2i−2i2i−2i−2i2i2-2-22-222-200000000000000000000
χ692-2-222-2-22-2222-2-22-200-22002i−2i−2i2i2i−2i−2i2i0000000000002-2-222-2-2200000000−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ702-2-222-2-22-2222-2-22-200-22002i−2i−2i2i2i−2i−2i2i000000000000-222-2-222-2000000002i−2i−2i2i2i−2i−2i2i00000000000000000000
χ712-2-222-2-22-2222-2-22-200-2200−2i2i2i−2i−2i2i2i−2i0000000000002-2-222-2-22000000002i−2i−2i2i2i−2i−2i2i00000000000000000000
χ722-2-222-2-22-2222-2-22-200-2200−2i2i2i−2i−2i2i2i−2i000000000000-222-2-222-200000000−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ732-2-222-2-22-222-222-2-2002-2000000000000002i−2i−2i2i−2i2i2i−2i2-2-22-222-20000000000000000−2i2i2i−2i2i−2i−2i2i000000000000
χ742-2-222-2-22-222-222-2-2002-2000000000000002i−2i−2i2i−2i2i2i−2i-222-22-2-2200000000000000002i−2i−2i2i−2i2i2i−2i000000000000
χ752-2-222-2-22-222-222-2-2002-200000000000000−2i2i2i−2i2i−2i−2i2i2-2-22-222-200000000000000002i−2i−2i2i−2i2i2i−2i000000000000
χ762-2-222-2-22-222-222-2-2002-200000000000000−2i2i2i−2i2i−2i−2i2i-222-22-2-220000000000000000−2i2i2i−2i2i−2i−2i2i000000000000
χ77444-4-4-4-4444-40000-4000000000000000000000000000000000000000000000000000000000000000022−220000
χ78444-4-4-4-4444-40000-40000000000000000000000000000000000000000000000000000000000000000−22220000
χ79444-4-4-4-44-4-4400004000000000000000000000000000000000000000000000000000000000000002i2−2i2000000
χ80444-4-4-4-44-4-440000400000000000000000000000000000000000000000000000000000000000000−2i22i2000000
χ814-4-4-4-44444-440000-400000000000000000000000000000000000000000000000000000000002i2−2i20000000000
χ824-4-4-4-44444-440000-40000000000000000000000000000000000000000000000000000000000−2i22i20000000000
χ834-4-4-4-4444-44-40000400000000000000000000000000000000000000000000000000000000000022−2200000000
χ844-4-4-4-4444-44-400004000000000000000000000000000000000000000000000000000000000000−222200000000
χ8588-88-8-88-8000000000000000000000000000000000000000000000000000000000000000000000000000000
χ868-888-88-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000

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