Finite Group Databasebeta

← Group #72322311

Character table — Group #72322311

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88
size111122222222222222222244444488888888888888881616161616161616161616161616161616161616161616161616161616161616161616163232323232323232
order12222222224444444488888888882222444488888888444444444444448888881616161616161616161616161616161624444488
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ311111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ411111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1
χ5111111111111111111111111111111-1-111-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111111111111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1
χ7111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111
χ8111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ91111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ101111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-11111
χ111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1
χ121111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111111111-1-1
χ131111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ141111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ151111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111
χ161111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111
χ17222222222222222222-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2000022000000000000-2-2000000000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-2-2-222-2-222-2-22222-2-2-2-20000-2-200000000000022000000000000000000000000
χ19222222222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-222222222220000-2-2000000000000-2-2000000000000000000000000
χ20222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200002200000000000022000000000000000000000000
χ21222222-2-2-2-2222-2-2-2-2222222-2-2-22-2000000000000000000000000002i2i−2i−2i2i2i−2i−2i000000000022-2-2000000000000
χ22222222-2-2-2-2222-2-2-2-2222222-2-2-22-2000000000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000-2-222000000000000
χ23222222-2-2-2-2222-2-2-2-2222222-2-2-22-200000000000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000-2-222000000000000
χ24222222-2-2-2-2222-2-2-2-2222222-2-2-22-200000000000000000000000000−2i−2i2i2i−2i−2i2i2i000000000022-2-2000000000000
χ252222-2-222-2-22-2-22-22-22-2-2-2-2222-22-2000000000000000022-2-20000002i−2i2i−2i0000000000000000002i2i−2i−2i00000000
χ262222-2-222-2-22-2-22-22-22-2-2-2-2222-22-2000000000000000022-2-2000000−2i2i−2i2i000000000000000000−2i−2i2i2i00000000
χ272222-2-222-2-22-2-22-22-22-2-2-2-2222-22-20000000000000000-2-2220000002i−2i2i−2i000000000000000000−2i−2i2i2i00000000
χ282222-2-222-2-22-2-22-22-22-2-2-2-2222-22-20000000000000000-2-222000000−2i2i−2i2i0000000000000000002i2i−2i−2i00000000
χ292222-2-2-2-2222-2-2-22-2222222-222-2-2-20000000022-2-2000000002-222-2-20000000000000000000000000000002-200
χ302222-2-2-2-2222-2-2-22-2222222-222-2-2-20000000022-2-2000000002-2-2-222000000000000000000000000000000-2200
χ312222-2-2-2-2222-2-2-22-2222222-222-2-2-200000000-2-22200000000-2222-2-2000000000000000000000000000000-2200
χ322222-2-2-2-2222-2-2-22-2222222-222-2-2-200000000-2-22200000000-22-2-2220000000000000000000000000000002-200
χ332222-2-2-2-2222-2-2-22-222-2-2-2-22-2-22220000000022-2-200000000-2200002-2-2200000000000000000000002-2000000
χ342222-2-2-2-2222-2-2-22-222-2-2-2-22-2-22220000000022-2-200000000-220000-222-20000000000000000000000-22000000
χ352222-2-2-2-2222-2-2-22-222-2-2-2-22-2-222200000000-2-222000000002-200002-2-220000000000000000000000-22000000
χ362222-2-2-2-2222-2-2-22-222-2-2-2-22-2-222200000000-2-222000000002-20000-222-200000000000000000000002-2000000
χ372-2-222-22-22-2-22-222-2-2222-2-222-2-2-22002-2002-2000000002i−2i2i−2i000000000000002-200000000000000000000002i−2i
χ382-2-222-22-22-2-22-222-2-2222-2-222-2-2-22002-2002-200000000−2i2i−2i2i000000000000002-20000000000000000000000−2i2i
χ392-2-222-22-22-2-22-222-2-2222-2-222-2-2-2200-2200-22000000002i−2i2i−2i00000000000000-220000000000000000000000−2i2i
χ402-2-222-22-22-2-22-222-2-2222-2-222-2-2-2200-2200-2200000000−2i2i−2i2i00000000000000-2200000000000000000000002i−2i
χ412-2-222-22-22-2-22-222-2-22-2-222-2-2222-2002-2002-200000000000000000000002i−2i2i−2i-220000000000000000002i−2i0000
χ422-2-222-22-22-2-22-222-2-22-2-222-2-2222-2002-2002-20000000000000000000000−2i2i−2i2i-22000000000000000000−2i2i0000
χ432-2-222-22-22-2-22-222-2-22-2-222-2-2222-200-2200-2200000000000000000000002i−2i2i−2i2-2000000000000000000−2i2i0000
χ442-2-222-22-22-2-22-222-2-22-2-222-2-2222-200-2200-220000000000000000000000−2i2i−2i2i2-20000000000000000002i−2i0000
χ452-2-222-2-22-22-22-2-2-2222-2-222-22-2-22200000000000000000000002-22-200002-2-2200000022-2-20000000000000000
χ462-2-222-2-22-22-22-2-2-2222-2-222-22-2-22200000000000000000000002-22-20000-222-2000000-2-2220000000000000000
χ472-2-222-2-22-22-22-2-2-2222-2-222-22-2-2220000000000000000000000-22-2200002-2-22000000-2-2220000000000000000
χ482-2-222-2-22-22-22-2-2-2222-2-222-22-2-2220000000000000000000000-22-220000-222-200000022-2-20000000000000000
χ492-2-22-222-2-22-2-222-2-222-2-22222-22-2-200000000000000002i−2i−2i2i002-2-2200000000002i2i−2i−2i00000000000000000000
χ502-2-22-222-2-22-2-222-2-222-2-22222-22-2-200000000000000002i−2i−2i2i00-222-20000000000−2i−2i2i2i00000000000000000000
χ512-2-22-222-2-22-2-222-2-222-2-22222-22-2-20000000000000000−2i2i2i−2i002-2-220000000000−2i−2i2i2i00000000000000000000
χ522-2-22-222-2-22-2-222-2-222-2-22222-22-2-20000000000000000−2i2i2i−2i00-222-200000000002i2i−2i−2i00000000000000000000
χ532-2-22-22-222-222-22-2-22-20000000000002-200-222i−2i2i−2i2i2i−2i−2i000000000000000000002−22−2i2−i2i2−i2i2−i2i2−i22−22−200000000
χ542-2-22-22-222-222-22-2-22-20000000000002-200-222i−2i2i−2i2i2i−2i−2i00000000000000000000−22−22−i2i2−i2i2−i2i2−i2i2−22−2200000000
χ552-2-22-22-222-222-22-2-22-20000000000002-200-22−2i2i−2i2i−2i−2i2i2i000000000000000000002−22−2−i2i2−i2i2−i2i2−i2i22−22−200000000
χ562-2-22-22-222-222-22-2-22-20000000000002-200-22−2i2i−2i2i−2i−2i2i2i00000000000000000000−22−22i2−i2i2−i2i2−i2i2−i2−22−2200000000
χ572-2-22-22-222-222-22-2-22-2000000000000-22002-22i−2i2i−2i−2i−2i2i2i000000000000000000002−22−2i2−i2i2−i2−i2i2−i2i2−22−2200000000
χ582-2-22-22-222-222-22-2-22-2000000000000-22002-22i−2i2i−2i−2i−2i2i2i00000000000000000000−22−22−i2i2−i2i2i2−i2i2−i22−22−200000000
χ592-2-22-22-222-222-22-2-22-2000000000000-22002-2−2i2i−2i2i2i2i−2i−2i000000000000000000002−22−2−i2i2−i2i2i2−i2i2−i2−22−2200000000
χ602-2-22-22-222-222-22-2-22-2000000000000-22002-2−2i2i−2i2i2i2i−2i−2i00000000000000000000−22−22i2−i2i2−i2−i2i2−i2i22−22−200000000
χ614444444444-4-4-4-4-4-4-4-400000000004400-4-4000000000000000000000000000000000000000000000000000000
χ624444444444-4-4-4-4-4-4-4-40000000000-4-40044000000000000000000000000000000000000000000000000000000
χ63444444-4-4-4-4444-4-4-4-44-4-4-4-4-4444-44000000000000000000000000000000000000000000000000000000000000
χ64444444-4-4-4-4-4-4-44444-400000000000000000000000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ65444444-4-4-4-4-4-4-44444-40000000000000000000000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ664444-4-444-4-44-4-44-44-444444-4-4-44-44000000000000000000000000000000000000000000000000000000000000
χ674444-4-444-4-4-444-44-44-4000000000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ684444-4-444-4-4-444-44-44-400000000000000000000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ694444-4-4-4-444-4444-44-4-40000000000004400-4-40000000000000000000000000000000000000000000000000000
χ704444-4-4-4-444-4444-44-4-4000000000000-4-400440000000000000000000000000000000000000000000000000000
χ714-4-444-44-44-44-44-4-444-40000000000000000004i−4i−4i4i000000000000000000000000000000000000000000000000
χ724-4-444-44-44-44-44-4-444-4000000000000000000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ734-4-444-4-44-444-4444-4-4-400000000000000000000000000000000000000000000000000000000002i2−2i2−2i22i200000000
χ744-4-444-4-44-444-4444-4-4-40000000000000000000000000000000000000000000000000000000000−2i22i22i2−2i200000000
χ754-4-444-4-44-44-44-4-4-444444-4-44-444-4-4000000000000000000000000000000000000000000000000000000000000
χ764-4-44-444-4-4444-4-444-4-40000000000000000000000000000000000000000000000000000002i2−2i2−2i22i2000000000000
χ774-4-44-444-4-4444-4-444-4-4000000000000000000000000000000000000000000000000000000−2i22i22i2−2i2000000000000
χ784-4-44-444-4-44-4-444-4-44444-4-4-4-44-444000000000000000000000000000000000000000000000000000000000000
χ794-4-44-44-444-4-4-44-444-4444-4-4-44-444-4000000000000000000000000000000000000000000000000000000000000
χ804-4-44-44-444-4-4-44-444-44-4-4444-44-4-44000000000000000000000000000000000000000000000000000000000000
χ8188-8-8000000000000004i2−4i24i2−4i200000000004i−4i00000022−2222−2200000000000000000000000000000000000000000000
χ8288-8-8000000000000004i2−4i24i2−4i20000000000−4i4i000000−2222−222200000000000000000000000000000000000000000000
χ8388-8-800000000000000−4i24i2−4i24i200000000004i−4i000000−2222−222200000000000000000000000000000000000000000000
χ8488-8-800000000000000−4i24i2−4i24i20000000000−4i4i00000022−2222−2200000000000000000000000000000000000000000000
χ858-88-8000000000000004i2−4i2−4i24i20000004-400000000002i2−2i2−2i22i200000000000000000000000000000000000000000000
χ868-88-8000000000000004i2−4i2−4i24i2000000-440000000000−2i22i22i2−2i200000000000000000000000000000000000000000000
χ878-88-800000000000000−4i24i24i2−4i20000004-40000000000−2i22i22i2−2i200000000000000000000000000000000000000000000
χ888-88-800000000000000−4i24i24i2−4i2000000-4400000000002i2−2i2−2i22i200000000000000000000000000000000000000000000

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