Finite Group Databasebeta

← Group #72322126

Character table — Group #72322126

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88
size111122222222222222222244444488888888888888881616161616161616161616161616161616161616161616161616161616161616161616163232323232323232
order12222222224444444488888888882244444488888888222222444444448888881616161616161616161616161616161622444488
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ5111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111
χ6111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ7111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-111
χ8111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1111111-1-1
χ91111111111111111111111111111-1-11111-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1
χ101111111111111111111111111111-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ111111111111111111111111111111-1-11111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ121111111111111111111111111111-1-11111-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-111
χ131111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1
χ141111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111
χ151111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1
χ161111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111
χ17222222222222222222-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-200000000000022-2-20000000000000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-2-2-222-2-2-2-22222222222000000000000-2-2-2-20000000000000000000000000000
χ19222222222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-22222000000000000-2-2220000000000000000000000000000
χ20222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-200000000000022220000000000000000000000000000
χ21222222-2-2-2-222-22-22-2-2-2-2-2-2222-22-2000000000000000022-2-20000000000002i2i−2i−2i0000000000002i2i−2i−2i00000000
χ22222222-2-2-2-222-22-22-2-2-2-2-2-2222-22-2000000000000000022-2-2000000000000−2i−2i2i2i000000000000−2i−2i2i2i00000000
χ23222222-2-2-2-222-22-22-2-2-2-2-2-2222-22-20000000000000000-2-2220000000000002i2i−2i−2i000000000000−2i−2i2i2i00000000
χ24222222-2-2-2-222-22-22-2-2-2-2-2-2222-22-20000000000000000-2-222000000000000−2i−2i2i2i0000000000002i2i−2i−2i00000000
χ252222-2-22-22-2-2-222-222-222222-2-2-22-200000000000000002-22-20022-2-200000000000000000022-2-2000000000000
χ262222-2-22-22-2-2-222-222-222222-2-2-22-200000000000000002-22-200-2-222000000000000000000-2-222000000000000
χ272222-2-22-22-2-2-222-222-222222-2-2-22-20000000000000000-22-220022-2-2000000000000000000-2-222000000000000
χ282222-2-22-22-2-2-222-222-222222-2-2-22-20000000000000000-22-2200-2-22200000000000000000022-2-2000000000000
χ292222-2-2-22-22-2-2-2222-222222-222-2-2-200000000000022-2-20000220000-2-22-200000000000000000000002-2000000
χ302222-2-2-22-22-2-2-2222-222222-222-2-2-200000000000022-2-20000-2-20000222-20000000000000000000000-22000000
χ312222-2-2-22-22-2-2-2222-222222-222-2-2-2000000000000-2-2220000220000-2-2-220000000000000000000000-22000000
χ322222-2-2-22-22-2-2-2222-222222-222-2-2-2000000000000-2-2220000-2-2000022-2200000000000000000000002-2000000
χ332222-2-2-22-22-2-2-2222-22-2-2-2-22-2-222200000000000022-2-22-2-2200000000-220000000000000000000000002-20000
χ342222-2-2-22-22-2-2-2222-22-2-2-2-22-2-222200000000000022-2-2-222-200000000-22000000000000000000000000-220000
χ352222-2-2-22-22-2-2-2222-22-2-2-2-22-2-2222000000000000-2-2222-2-22000000002-2000000000000000000000000-220000
χ362222-2-2-22-22-2-2-2222-22-2-2-2-22-2-2222000000000000-2-222-222-2000000002-20000000000000000000000002-20000
χ372-2-222-222-2-22-2-2-2222-222-2-2-22-222-2000000000000000000002-200002-200002i−2i2i−2i00002i2i−2i−2i0000000000000000
χ382-2-222-222-2-22-2-2-2222-222-2-2-22-222-2000000000000000000002-200002-20000−2i2i−2i2i0000−2i−2i2i2i0000000000000000
χ392-2-222-222-2-22-2-2-2222-222-2-2-22-222-200000000000000000000-220000-2200002i−2i2i−2i0000−2i−2i2i2i0000000000000000
χ402-2-222-222-2-22-2-2-2222-222-2-2-22-222-200000000000000000000-220000-220000−2i2i−2i2i00002i2i−2i−2i0000000000000000
χ412-2-222-2-2-2222-22-2-22-2222-2-22-222-2-22-200002-2000000000000002i−2i2i−2i00002-2000000000000000000000000002i−2i
χ422-2-222-2-2-2222-22-2-22-2222-2-22-222-2-22-200002-200000000000000−2i2i−2i2i00002-200000000000000000000000000−2i2i
χ432-2-222-2-2-2222-22-2-22-2222-2-22-222-2-2-220000-22000000000000002i−2i2i−2i0000-2200000000000000000000000000−2i2i
χ442-2-222-2-2-2222-22-2-22-2222-2-22-222-2-2-220000-2200000000000000−2i2i−2i2i0000-22000000000000000000000000002i−2i
χ452-2-222-2-2-2222-22-2-22-22-2-222-22-2-2222-200002-20000000000000000000000-222-2-22000000000000000000002-200
χ462-2-222-2-2-2222-22-2-22-22-2-222-22-2-2222-200002-20000000000000000000000-22-222-200000000000000000000-2200
χ472-2-222-2-2-2222-22-2-22-22-2-222-22-2-222-220000-2200000000000000000000002-22-2-2200000000000000000000-2200
χ482-2-222-2-2-2222-22-2-22-22-2-222-22-2-222-220000-2200000000000000000000002-2-222-2000000000000000000002-200
χ492-2-22-222-2-222-2222-2-2-200000000002-20000-2222-2-22-22-200000000000000000000i2i2−i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000
χ502-2-22-222-2-222-2222-2-2-200000000002-20000-2222-2-22-22-200000000000000000000−i2−i2i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000
χ512-2-22-222-2-222-2222-2-2-200000000002-20000-22-2-222-22-2200000000000000000000i2i2−i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i200000000
χ522-2-22-222-2-222-2222-2-2-200000000002-20000-22-2-222-22-2200000000000000000000−i2−i2i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i200000000
χ532-2-22-222-2-222-2222-2-2-20000000000-2200002-222-2-2-22-2200000000000000000000i2i2−i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i200000000
χ542-2-22-222-2-222-2222-2-2-20000000000-2200002-222-2-2-22-2200000000000000000000−i2−i2i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i200000000
χ552-2-22-222-2-222-2222-2-2-20000000000-2200002-2-2-2222-22-200000000000000000000i2i2−i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200000000
χ562-2-22-222-2-222-2222-2-2-20000000000-2200002-2-2-2222-22-200000000000000000000−i2−i2i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200000000
χ572-2-22-22-222-2-222-222-2-222-2-222-2-2-22000000000000000000002-22i−2i−2i2i-22000000002i−2i2i−2i00000000000000000000
χ582-2-22-22-222-2-222-222-2-222-2-222-2-2-22000000000000000000002-2−2i2i2i−2i-2200000000−2i2i−2i2i00000000000000000000
χ592-2-22-22-222-2-222-222-2-222-2-222-2-2-2200000000000000000000-222i−2i−2i2i2-200000000−2i2i−2i2i00000000000000000000
χ602-2-22-22-222-2-222-222-2-222-2-222-2-2-2200000000000000000000-22−2i2i2i−2i2-2000000002i−2i2i−2i00000000000000000000
χ614444444444-4-4-4-4-4-4-4-400000000000044-4-4000000000000000000000000000000000000000000000000000000
χ624444444444-4-4-4-4-4-4-4-4000000000000-4-444000000000000000000000000000000000000000000000000000000
χ63444444-4-4-4-444-44-44-4-44444-4-4-44-44000000000000000000000000000000000000000000000000000000000000
χ64444444-4-4-4-4-4-44-44-444000000000000000000000000000000000000000000000022−22−222200000000000000000000
χ65444444-4-4-4-4-4-44-44-4440000000000000000000000000000000000000000000000−222222−2200000000000000000000
χ664444-4-44-44-444-4-44-4-440000000000000000000000000000000000000000000000000022−22−22220000000000000000
χ674444-4-44-44-444-4-44-4-4400000000000000000000000000000000000000000000000000−222222−220000000000000000
χ684444-4-44-44-4-4-444-444-4-4-4-4-4-4444-44000000000000000000000000000000000000000000000000000000000000
χ694444-4-4-44-44444-4-4-44-40000000000440000-4-40000000000000000000000000000000000000000000000000000
χ704444-4-4-44-44444-4-4-44-40000000000-4-40000440000000000000000000000000000000000000000000000000000
χ714-4-444-444-4-44-4-4-4444-4-4-4444-44-4-44000000000000000000000000000000000000000000000000000000000000
χ724-4-444-444-4-4-4444-4-4-440000000000000000000000000000000000000000000000000000002i2−2i2−2i22i2000000000000
χ734-4-444-444-4-4-4444-4-4-44000000000000000000000000000000000000000000000000000000−2i22i22i2−2i2000000000000
χ744-4-444-4-4-444-44-444-44-400000000000000000000004-4-4400000000000000000000000000000000000000000000
χ754-4-444-4-4-444-44-444-44-40000000000000000000000-444-400000000000000000000000000000000000000000000
χ764-4-44-444-4-44-44-4-4-444444-4-4-4-44-444000000000000000000000000000000000000000000000000000000000000
χ774-4-44-444-4-44-44-4-4-4444-4-44444-44-4-4000000000000000000000000000000000000000000000000000000000000
χ784-4-44-44-444-44-4-44-4-444000000000000000000000000000000000000000000000000000000000022−22−222200000000
χ794-4-44-44-444-44-4-44-4-4440000000000000000000000000000000000000000000000000000000000−222222−2200000000
χ804-4-44-44-444-4-444-444-4-4-4-444-4-4444-4000000000000000000000000000000000000000000000000000000000000
χ8188-8-80000000000000042−4242−4200000000004-40022−2222−22000000000000000000000000000000000000000000000000
χ8288-8-80000000000000042−4242−420000000000-4400−2222−2222000000000000000000000000000000000000000000000000
χ8388-8-800000000000000−4242−424200000000004-400−2222−2222000000000000000000000000000000000000000000000000
χ8488-8-800000000000000−4242−42420000000000-440022−2222−22000000000000000000000000000000000000000000000000
χ858-88-80000000000000042−42−4242000000004-4000022−22−2222000000000000000000000000000000000000000000000000
χ868-88-80000000000000042−42−424200000000-440000−222222−22000000000000000000000000000000000000000000000000
χ878-88-800000000000000−424242−42000000004-40000−222222−22000000000000000000000000000000000000000000000000
χ888-88-800000000000000−424242−4200000000-44000022−22−2222000000000000000000000000000000000000000000000000

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