Finite Group Databasebeta

← Group #72319722

Character table — Group #72319722

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size112222222444444888888888881616161616161616161616161616161616161616323232323232323232323232323232323232
order1222222224444442222222244422444444444444448888444444444488888888
χ11111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111
χ511111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1
χ611111111111111111111111111-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1111111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1
χ911-1-1111-1-111-1-1-1-1111-1-1-11-111-11-11-11111-1-1-1-1ii−i−iii−i−ii−i11-1-1ii−i−i1-1i−iii−i−i
χ1011-1-1111-1-111-1-1-1-1111-1-1-11-111-11-11-11111-1-1-1-1−i−iii−i−iii−ii11-1-1−i−iii1-1−ii−i−iii
χ1111-1-1111-1-111-1-1-1-1111-1-1-11-111-11-11-1-1-1-1-11111ii−i−iii−i−ii−i-1-111−i−iii1-1i−i−i−iii
χ1211-1-1111-1-111-1-1-1-1111-1-1-11-111-11-11-1-1-1-1-11111−i−iii−i−iii−ii-1-111ii−i−i1-1−iiii−i−i
χ1311-1-1111-1-111-1-1-1-1111-1-1-11-111-1-11-111111-1-1-1-1ii−i−i−i−iii−ii-1-111ii−i−i-11i−i−i−iii
χ1411-1-1111-1-111-1-1-1-1111-1-1-11-111-1-11-111111-1-1-1-1−i−iiiii−i−ii−i-1-111−i−iii-11−iiii−i−i
χ1511-1-1111-1-111-1-1-1-1111-1-1-11-111-1-11-11-1-1-1-11111ii−i−i−i−iii−ii11-1-1−i−iii-11i−iii−i−i
χ1611-1-1111-1-111-1-1-1-1111-1-1-11-111-1-11-11-1-1-1-11111−i−iiiii−i−ii−i11-1-1ii−i−i-11−ii−i−iii
χ17222222222222222-2-2-2-2-2-2-2-222200000000000000002222-2-20000000000000000
χ18222222222222222-2-2-2-2-2-2-2-22220000000000000000-2-2-2-2220000000000000000
χ192222222222222-2-222-22-2-2-22-2-2-200000000000022220000000000000000-2-20000
χ202222222222222-2-222-22-2-2-22-2-2-2000000000000-2-2-2-20000000000000000220000
χ212222222222222-2-2-2-22-2222-2-2-2-2222200000000000000000000000000-2-2000000
χ222222222222222-2-2-2-22-2222-2-2-2-2-2-2-2-20000000000000000000000000022000000
χ23222-22-2-22-2-222-2222-2222-2-2-22-2-200000000000000000000002i−2i2i−2i000000000000
χ24222-22-2-22-2-222-2222-2222-2-2-22-2-20000000000000000000000−2i2i−2i2i000000000000
χ25222-22-2-22-2-222-222-22-2-2-22222-2-2000000000000000000000000002-22-200000000
χ26222-22-2-22-2-222-222-22-2-2-22222-2-200000000000000000000000000-22-2200000000
χ27222-22-2-22-2-222-2-2-22-2-22-222-2-22200000000000000000000000000000000002i−2i2i−2i
χ28222-22-2-22-2-222-2-2-22-2-22-222-2-2220000000000000000000000000000000000−2i2i−2i2i
χ29222-22-2-22-2-222-2-2-2-222-22-2-22-22200002i2i−2i−2i2i2i−2i−2i00000000000000000000000000
χ30222-22-2-22-2-222-2-2-2-222-22-2-22-2220000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000
χ3122-222-2-2-22-22-22222-2-2-22-222-22-200000000000000000000000000000000002-2-22
χ3222-222-2-2-22-22-22222-2-2-22-222-22-20000000000000000000000000000000000-222-2
χ3322-222-2-2-22-22-2222-2222-22-2-2-22-200002i2i−2i−2i−2i−2i2i2i00000000000000000000000000
χ3422-222-2-2-22-22-2222-2222-22-2-2-22-20000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000
χ3522-222-2-2-22-22-22-2-22-22-2-22-222-2200000000000000000000002i−2i−2i2i000000000000
χ3622-222-2-2-22-22-22-2-22-22-2-22-222-220000000000000000000000−2i2i2i−2i000000000000
χ3722-222-2-2-22-22-22-2-2-22-222-22-22-22000000000000000000000000002i−2i−2i2i00000000
χ3822-222-2-2-22-22-22-2-2-22-222-22-22-2200000000000000000000000000−2i2i2i−2i00000000
χ3922-2-2222-2-222-2-22222-2-222-2-2-2-220000000000002i2i−2i−2i0000000000000000−2i2i0000
χ4022-2-2222-2-222-2-22222-2-222-2-2-2-22000000000000−2i−2i2i2i00000000000000002i−2i0000
χ4122-2-2222-2-222-2-222-2-222-2-222-2-222-22-200000000000000000000000000-22000000
χ4222-2-2222-2-222-2-222-2-222-2-222-2-22-22-22000000000000000000000000002-2000000
χ4322-2-2222-2-222-2-2-2-2-2-2-2222-2222-200000000000000002i2i−2i−2i−2i2i0000000000000000
χ4422-2-2222-2-222-2-2-2-2-2-2-2222-2222-20000000000000000−2i−2i2i2i2i−2i0000000000000000
χ45444444444-4-4-4-4000000000000000002-22-22-22-200000000000000000000000000
χ46444444444-4-4-4-400000000000000000-22-22-22-2200000000000000000000000000
χ474444-44-4-4-40000000000000000022-2-2000000002i−2i2i−2i2i−2i2i−2i000000000000000000
χ484444-44-4-4-40000000000000000022-2-200000000−2i2i−2i2i−2i2i−2i2i000000000000000000
χ494444-44-4-4-400000000000000000-2-222000000002i−2i2i−2i−2i2i−2i2i000000000000000000
χ504444-44-4-4-400000000000000000-2-22200000000−2i2i−2i2i2i−2i2i−2i000000000000000000
χ51444-44-4-44-44-4-44000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000000000
χ52444-44-4-44-44-4-4400000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000
χ5344-444-4-4-444-44-4000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ5444-444-4-4-444-44-400000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ5544-4-4444-4-4-4-444000000000000000002-22-2-22-2200000000000000000000000000
χ5644-4-4444-4-4-4-44400000000000000000-22-222-22-200000000000000000000000000
χ5744-4-4-44-444000000000000000002-2-22000000002-2-222-2-22000000000000000000
χ5844-4-4-44-444000000000000000002-2-2200000000-222-2-222-2000000000000000000
χ5944-4-4-44-44400000000000000000-222-2000000002-2-22-222-2000000000000000000
χ6044-4-4-44-44400000000000000000-222-200000000-222-22-2-22000000000000000000
χ61888-8-8-88-880000000000000000000000000000000000000000000000000000000
χ6288-88-8-888-80000000000000000000000000000000000000000000000000000000
χ6316-16000000000008-80000000000000000000000000000000000000000000000000
χ6416-1600000000000-880000000000000000000000000000000000000000000000000

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