Finite Group Databasebeta

← Group #72257237

Character table — Group #72257237

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88
size11112222222222222222224444444444888888888816161616161616161616161616161616161616161616161616161616161616161616161616163232323232323232
order12222222224444444488882222888888444444888822222222224444444488881616161616161616161616161616161644448888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1
χ511111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1
χ611111111111111111111111111111111-1-1-1-111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1
χ711111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11111
χ811111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111111
χ91111111111111111111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ101111111111111111111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111
χ121111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-111
χ131111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ141111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ151111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ161111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ17222222222222222222-2-2-2-22222-2-2-2-2-2-2222222-2-2-2-2000000000000000022-2-2-2-2000000000000000000000000
χ18222222222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-222-2-2-2-20000000000000000-2-22222000000000000000000000000
χ19222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-222220000000000000000-2-2-2-222000000000000000000000000
χ20222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000002222-2-2000000000000000000000000
χ2122222-2-2-22-22-2-22-222-2222200002-2-2-22-20000000000000022-2-2220000-2-20000000000000022-2-2000000000000
χ2222222-2-2-22-22-2-22-222-2222200002-2-2-22-20000000000000022-2-2-2-200002200000000000000-2-222000000000000
χ2322222-2-2-22-22-2-22-222-2222200002-2-2-22-200000000000000-2-222220000-2-200000000000000-2-222000000000000
χ2422222-2-2-22-22-2-22-222-2222200002-2-2-22-200000000000000-2-222-2-20000220000000000000022-2-2000000000000
χ252222-22-2-2-22-22-22-22-2222220000-22-2-2-22000000000022-2-200000022-2-20000000000000000000022-2-200000000
χ262222-22-2-2-22-22-22-22-2222220000-22-2-2-22000000000022-2-2000000-2-22200000000000000000000-2-22200000000
χ272222-22-2-2-22-22-22-22-2222220000-22-2-2-220000000000-2-22200000022-2-200000000000000000000-2-22200000000
χ282222-22-2-2-22-22-22-22-2222220000-22-2-2-220000000000-2-222000000-2-2220000000000000000000022-2-200000000
χ292-2-2222-22-2-22-2-2-222-2222-2-20000-222-22-2000000000000002-22-2002i−2i2i−2i0000000000002i2i−2i−2i0000000000000000
χ302-2-2222-22-2-22-2-2-222-2222-2-20000-222-22-2000000000000002-22-200−2i2i−2i2i000000000000−2i−2i2i2i0000000000000000
χ312-2-2222-22-2-22-2-2-222-2222-2-20000-222-22-200000000000000-22-22002i−2i2i−2i000000000000−2i−2i2i2i0000000000000000
χ322-2-2222-22-2-22-2-2-222-2222-2-20000-222-22-200000000000000-22-2200−2i2i−2i2i0000000000002i2i−2i−2i0000000000000000
χ332-2-222-22-2-22222-2-22-2-222-2-20000-2-2-22222i2i−2i−2i00000000002-2-2200000000002i−2i0000000000000000000000002i−2i
χ342-2-222-22-2-22222-2-22-2-222-2-20000-2-2-22222i2i−2i−2i0000000000-222-200000000002i−2i000000000000000000000000−2i2i
χ352-2-222-22-2-22222-2-22-2-222-2-20000-2-2-2222−2i−2i2i2i00000000002-2-220000000000−2i2i000000000000000000000000−2i2i
χ362-2-222-22-2-22222-2-22-2-222-2-20000-2-2-2222−2i−2i2i2i0000000000-222-20000000000−2i2i0000000000000000000000002i−2i
χ372-2-222-22-2-22222-2-22-2-2-2-2220000222-2-2-22i2i−2i−2i0000002-22-200000000000000−2i2i00000000000000000000002i−2i00
χ382-2-222-22-2-22222-2-22-2-2-2-2220000222-2-2-22i2i−2i−2i000000-22-2200000000000000−2i2i0000000000000000000000−2i2i00
χ392-2-222-22-2-22222-2-22-2-2-2-2220000222-2-2-2−2i−2i2i2i0000002-22-2000000000000002i−2i0000000000000000000000−2i2i00
χ402-2-222-22-2-22222-2-22-2-2-2-2220000222-2-2-2−2i−2i2i2i000000-22-22000000000000002i−2i00000000000000000000002i−2i00
χ412-2-22-222-22-222-222-2-2-2000022-2-20000002i−2i2i−2i2-2000000000000000000002i−2i000022−2−2i2−i2i2−i22−22−2i2−i2i2−i200000000
χ422-2-22-222-22-222-222-2-2-2000022-2-20000002i−2i2i−2i2-2000000000000000000002i−2i0000−2−222−i2i2−i2i2−22−22−i2i2−i2i200000000
χ432-2-22-222-22-222-222-2-2-2000022-2-2000000−2i2i−2i2i2-200000000000000000000−2i2i000022−2−2−i2i2−i2i22−22−2−i2i2−i2i200000000
χ442-2-22-222-22-222-222-2-2-2000022-2-2000000−2i2i−2i2i2-200000000000000000000−2i2i0000−2−222i2−i2i2−i2−22−22i2−i2i2−i200000000
χ452-2-22-222-22-222-222-2-2-20000-2-2220000002i−2i2i−2i-2200000000000000000000−2i2i000022−2−2−i2i2−i2i2−22−22i2−i2i2−i200000000
χ462-2-22-222-22-222-222-2-2-20000-2-2220000002i−2i2i−2i-2200000000000000000000−2i2i0000−2−222i2−i2i2−i22−22−2−i2i2−i2i200000000
χ472-2-22-222-22-222-222-2-2-20000-2-222000000−2i2i−2i2i-22000000000000000000002i−2i000022−2−2i2−i2i2−i2−22−22−i2i2−i2i200000000
χ482-2-22-222-22-222-222-2-2-20000-2-222000000−2i2i−2i2i-22000000000000000000002i−2i0000−2−222−i2i2−i2i22−22−2i2−i2i2−i200000000
χ492-2-22-222-22-2-2-22-2-222222-2-222-2-222-22-2-20000-2222-2-200000000002i−2i−2i2i000000000000000000000000002i−2i0000
χ502-2-22-222-22-2-2-22-2-222222-2-222-2-222-22-2-20000-2222-2-20000000000−2i2i2i−2i00000000000000000000000000−2i2i0000
χ512-2-22-222-22-2-2-22-2-222222-2-2-2-22222-22-2-200002-2-2-22200000000002i−2i−2i2i00000000000000000000000000−2i2i0000
χ522-2-22-222-22-2-2-22-2-222222-2-2-2-22222-22-2-200002-2-2-2220000000000−2i2i2i−2i000000000000000000000000002i−2i0000
χ532-2-22-222-22-2-2-22-2-2222-2-22222-2-2-2-22-2220000-22-2-222000000002-200002-200000000000000000000002-2000000
χ542-2-22-222-22-2-2-22-2-2222-2-22222-2-2-2-22-2220000-22-2-22200000000-220000-220000000000000000000000-22000000
χ552-2-22-222-22-2-2-22-2-2222-2-222-2-222-2-22-22200002-222-2-2000000002-200002-20000000000000000000000-22000000
χ562-2-22-222-22-2-2-22-2-2222-2-222-2-222-2-22-22200002-222-2-200000000-220000-2200000000000000000000002-2000000
χ572-2-22-2-2-2222-22-2-2222-2-2-2220000-22-222-200000000002-2-2200002-20000-220000002-22-200000000000000000000
χ582-2-22-2-2-2222-22-2-2222-2-2-2220000-22-222-200000000002-2-220000-2200002-2000000-22-2200000000000000000000
χ592-2-22-2-2-2222-22-2-2222-2-2-2220000-22-222-20000000000-222-200002-20000-22000000-22-2200000000000000000000
χ602-2-22-2-2-2222-22-2-2222-2-2-2220000-22-222-20000000000-222-20000-2200002-20000002-22-200000000000000000000
χ614444444444-4-4-4-4-4-4-4-4000044440000000000-4-400000000000000000000000000000000000000000000000000
χ624444444444-4-4-4-4-4-4-4-40000-4-4-4-400000000004400000000000000000000000000000000000000000000000000
χ6344444-4-4-44-44-4-44-444-4-4-4-4-40000-4444-4400000000000000000000000000000000000000000000000000000000
χ6444444-4-4-44-4-444-44-4-44000000000000000000000000000000000000000000000022−22−222200000000000000000000
χ6544444-4-4-44-4-444-44-4-440000000000000000000000000000000000000000000000−222222−2200000000000000000000
χ664444-44-4-4-444-44-44-44-40000000000000000000000000000000000000000000000000022−22−22220000000000000000
χ674444-44-4-4-444-44-44-44-400000000000000000000000000000000000000000000000000−222222−220000000000000000
χ684444-44-4-4-44-44-44-44-44-4-4-4-400004-4444-400000000000000000000000000000000000000000000000000000000
χ694444-4-444-4-444-4-4-4-444000000000000004-4-440000000000000000000000000000000000000000000000000000
χ704444-4-444-4-444-4-4-4-44400000000000000-444-40000000000000000000000000000000000000000000000000000
χ714444-4-444-4-4-4-44444-4-444440000-4-444-4-400000000000000000000000000000000000000000000000000000000
χ724444-4-444-4-4-4-44444-4-4-4-4-4-4000044-4-44400000000000000000000000000000000000000000000000000000000
χ734-4-4444-44-4-44-4-4-444-44-4-44400004-4-44-4400000000000000000000000000000000000000000000000000000000
χ744-4-4444-44-4-4-4444-4-44-400000000000000000000000000000000000000000000000000000000002i2−2i2−2i22i200000000
χ754-4-4444-44-4-4-4444-4-44-40000000000000000000000000000000000000000000000000000000000−2i22i22i2−2i200000000
χ764-4-444-44-4-44-4-4-444-444000000000000000000000000000000000000000000004-4000000000000000000000000
χ774-4-444-44-4-44-4-4-444-44400000000000000000000000000000000000000000000-44000000000000000000000000
χ784-4-44-4-4-44444-444-4-4-4400000000000000000000000000000000000000000000000000000022−22−2222000000000000
χ794-4-44-4-4-44444-444-4-4-44000000000000000000000000000000000000000000000000000000−222222−22000000000000
χ804-4-44-4-4-4444-44-4-4444-444-4-400004-44-4-4400000000000000000000000000000000000000000000000000000000
χ8188-8-80000000000000042−4242−424-44-400000000000022−2222−220000000000000000000000000000000000000000000000
χ8288-8-80000000000000042−4242−42-44-44000000000000−2222−22220000000000000000000000000000000000000000000000
χ8388-8-800000000000000−4242−42424-44-4000000000000−2222−22220000000000000000000000000000000000000000000000
χ8488-8-800000000000000−4242−4242-44-4400000000000022−2222−220000000000000000000000000000000000000000000000
χ858-88-80000000000000042−42−42424-4-4400000000000022−22−22220000000000000000000000000000000000000000000000
χ868-88-80000000000000042−42−4242-444-4000000000000−222222−220000000000000000000000000000000000000000000000
χ878-88-800000000000000−424242−424-4-44000000000000−222222−220000000000000000000000000000000000000000000000
χ888-88-800000000000000−424242−42-444-400000000000022−22−22220000000000000000000000000000000000000000000000

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