Finite Group Databasebeta

← Group #72286738

Character table — Group #72286738

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size112222222444444888888888881616161616161616161616161616161616161616323232323232323232323232323232323232
order1222244442244442222444444422222244444444444444444488888888888888
χ11111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ4111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-1
χ511111111111111111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111
χ711111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111
χ911-1-1111-1-11-11-1-1-11-1-1111-111-1-111-1-11-11-1ii−i−i11-1-1ii−i−i11-1-1i−i1-1i−iii−i−iii−i−i
χ1011-1-1111-1-11-11-1-1-11-1-1111-111-1-111-1-11-11-1−i−iii11-1-1−i−iii11-1-1−ii1-1−ii−i−iii−i−iii
χ1111-1-1111-1-11-11-1-1-11-1-1111-111-1-111-1-1-11-11ii−i−i11-1-1−i−iii-1-111−ii-11i−i−i−iiiii−i−i
χ1211-1-1111-1-11-11-1-1-11-1-1111-111-1-111-1-1-11-11−i−iii11-1-1ii−i−i-1-111i−i-11−iiii−i−i−i−iii
χ1311-1-1111-1-11-11-1-1-11-1-1111-111-1-1-1-1111-11-1ii−i−i-1-111ii−i−i-1-111i−i1-1i−i−i−iii−i−iii
χ1411-1-1111-1-11-11-1-1-11-1-1111-111-1-1-1-1111-11-1−i−iii-1-111−i−iii-1-111−ii1-1−iiii−i−iii−i−i
χ1511-1-1111-1-11-11-1-1-11-1-1111-111-1-1-1-111-11-11ii−i−i-1-111−i−iii11-1-1−ii-11i−iii−i−i−i−iii
χ1611-1-1111-1-11-11-1-1-11-1-1111-111-1-1-1-111-11-11−i−iii-1-111ii−i−i11-1-1i−i-11−ii−i−iiiii−i−i
χ17222222222222222-2-2-2-2-2-2-2222-2000000000000000022220000-2-2000000000000
χ18222222222222222-2-2-2-2-2-2-2222-20000000000000000-2-2-2-2000022000000000000
χ192222222222222-2-222-2-22-2-2-2-2-220000000022220000000000000000-2-200000000
χ202222222222222-2-222-2-22-2-2-2-2-2200000000-2-2-2-200000000000000002200000000
χ212222222222222-2-2-2-222-222-2-2-2-200002222000000000000000000-2-20000000000
χ222222222222222-2-2-2-222-222-2-2-2-20000-2-2-2-2000000000000000000220000000000
χ2322222-2-2-2-2-2-222222222-2-2-22-2-2-2000000000000000000002-22-200000000000000
χ2422222-2-2-2-2-2-222222222-2-2-22-2-2-200000000000000000000-22-2200000000000000
χ2522222-2-2-2-2-2-22222-2-2-2-22222-2-2200000000000000000000000000000000002-22-2
χ2622222-2-2-2-2-2-22222-2-2-2-22222-2-220000000000000000000000000000000000-22-22
χ2722222-2-2-2-2-2-222-2-222-2-2-222-222-20000000000000000000000000000002i−2i2i−2i0000
χ2822222-2-2-2-2-2-222-2-222-2-2-222-222-2000000000000000000000000000000−2i2i−2i2i0000
χ2922222-2-2-2-2-2-222-2-2-2-2222-2-2-22222-22-2000000002-22-20000000000000000000000
χ3022222-2-2-2-2-2-222-2-2-2-2222-2-2-2222-22-2200000000-22-220000000000000000000000
χ3122-2-2222-2-22-22-2222-22-22-22-2-22-2000000002i2i−2i−2i0000000000000000−2i2i00000000
χ3222-2-2222-2-22-22-2222-22-22-22-2-22-200000000−2i−2i2i2i00000000000000002i−2i00000000
χ3322-2-2222-2-22-22-222-22-22-22-2-2-22200002-22-2000000000000000000-220000000000
χ3422-2-2222-2-22-22-222-22-22-22-2-2-2220000-22-220000000000000000002-20000000000
χ3522-2-2222-2-22-22-2-2-2-222-2-2-2222-2200000000000000002i2i−2i−2i0000−2i2i000000000000
χ3622-2-2222-2-22-22-2-2-2-222-2-2-2222-220000000000000000−2i−2i2i2i00002i−2i000000000000
χ3722-2-22-2-222-222-2222-22-2-22-2-22-220000000000000000000000000000002-2-220000
χ3822-2-22-2-222-222-2222-22-2-22-2-22-22000000000000000000000000000000-222-20000
χ3922-2-22-2-222-222-222-22-222-22-22-2-22-2-22000000002-2-220000000000000000000000
χ4022-2-22-2-222-222-222-22-222-22-22-2-2-222-200000000-222-20000000000000000000000
χ4122-2-22-2-222-222-2-2-22-2-22-2-222-222000000000000000000002-2-2200000000000000
χ4222-2-22-2-222-222-2-2-22-2-22-2-222-22200000000000000000000-222-200000000000000
χ4322-2-22-2-222-222-2-2-2-222-222-22-22-200000000000000000000000000000000002i−2i−2i2i
χ4422-2-22-2-222-222-2-2-2-222-222-22-22-20000000000000000000000000000000000−2i2i2i−2i
χ45444444444-4-4-4-40000000000000222200000000-2-2-2-20000000000000000000000
χ46444444444-4-4-4-40000000000000-2-2-2-20000000022220000000000000000000000
χ4744444-4-4-4-444-4-400000000000002-22-200000000-22-220000000000000000000000
χ4844444-4-4-4-444-4-40000000000000-22-22000000002-22-20000000000000000000000
χ49444-4-44-44-400000000000000000000022-2-22i−2i2i−2i00002i−2i2i−2i000000000000000000
χ50444-4-44-44-400000000000000000000022-2-2−2i2i−2i2i0000−2i2i−2i2i000000000000000000
χ51444-4-44-44-4000000000000000000000-2-2222i−2i2i−2i0000−2i2i−2i2i000000000000000000
χ52444-4-44-44-4000000000000000000000-2-222−2i2i−2i2i00002i−2i2i−2i000000000000000000
χ5344-44-44-4-440000000000000000000002-2-222-2-2200002-2-22000000000000000000
χ5444-44-44-4-440000000000000000000002-2-22-222-20000-222-2000000000000000000
χ5544-44-44-4-44000000000000000000000-222-22-2-220000-222-2000000000000000000
χ5644-44-44-4-44000000000000000000000-222-2-222-200002-2-22000000000000000000
χ5744-4-4444-4-4-44-44000000000000022-2-200000000-2-2220000000000000000000000
χ5844-4-4444-4-4-44-440000000000000-2-2220000000022-2-20000000000000000000000
χ5944-4-44-4-4444-4-4400000000000002-2-2200000000-222-20000000000000000000000
χ6044-4-44-4-4444-4-440000000000000-222-2000000002-2-220000000000000000000000
χ61888-8-8-88-880000000000000000000000000000000000000000000000000000000
χ6288-88-8-888-80000000000000000000000000000000000000000000000000000000
χ6316-16000000000008-80000000000000000000000000000000000000000000000000
χ6416-1600000000000-880000000000000000000000000000000000000000000000000

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