Finite Group Databasebeta

← Group #72240540

Character table — Group #72240540

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size1122222224444444444888888888161616161616161616161616161616163232323232323232323232323232323232323232
order1222244442222224444222244444222244444444444444444444444488888888
χ11111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ9111111111-111-1-1-111-1-111-1-111-1-1-1111-1111-1-1-1-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ10111111111-111-1-1-111-1-111-1-111-1-1-1111-1111-1-1-1-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ11111111111-111-1-1-111-1-111-1-111-1-1-111-1111-11-1-1-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ12111111111-111-1-1-111-1-111-1-111-1-1-111-1111-11-1-1-1-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ13111111111-111-1-1-111-1-111-1-111-1-1-1-1-11-1-1-11-1111111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ14111111111-111-1-1-111-1-111-1-111-1-1-1-1-11-1-1-11-1111111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ15111111111-111-1-1-111-1-111-1-111-1-1-1-1-1-11-1-1-111111-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ16111111111-111-1-1-111-1-111-1-111-1-1-1-1-1-11-1-1-111111-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222222-2-2222-2-2-2-22-2-2-22-22002-2002-20000-2-22200000000000000000000
χ18222222222222-2-2222-2-2-2-22-2-2-22-2200-2200-22000022-2-200000000000000000000
χ192222222222-2-2222-2-2222-2-2-22-22-2-2000000000000000000002-22-2000000000000
χ202222222222-2-2222-2-2222-2-2-22-22-2-200000000000000000000-22-22000000000000
χ212222222222-2-2-2-22-2-2-2-2-22-22-2222-200000000000000000000000000002i−2i2i−2i0000
χ222222222222-2-2-2-22-2-2-2-2-22-22-2222-20000000000000000000000000000−2i2i−2i2i0000
χ23222222222-22222-22222-2-2-22-2-2-22-2002200220000-2-2-2-200000000000000000000
χ24222222222-22222-22222-2-2-22-2-2-22-200-2-200-2-20000222200000000000000000000
χ25222222222-2-2-222-2-2-222-222-2-22-2-2200000000000000000000000000002-2-220000
χ26222222222-2-2-222-2-2-222-222-2-22-2-220000000000000000000000000000-222-20000
χ27222222222-2-2-2-2-2-2-2-2-2-22-2222-2-222000000000000000000002i−2i−2i2i000000000000
χ28222222222-2-2-2-2-2-2-2-2-2-22-2222-2-22200000000000000000000−2i2i2i−2i000000000000
χ2922222-2-2-2-2222222-2-2-2-22-22-2-22-22-22-2002-20022-2-2000000000000000000000000
χ3022222-2-2-2-2222222-2-2-2-22-22-2-22-22-2-2200-2200-2-222000000000000000000000000
χ3122222-2-2-2-2222-2-22-2-222-22222-2-2-2-200000000000000002-22-20000000000000000
χ3222222-2-2-2-2222-2-22-2-222-22222-2-2-2-20000000000000000-22-220000000000000000
χ3322222-2-2-2-22-2-222222-2-222-22-2-2-2-220000000000000000000000002-22-200000000
χ3422222-2-2-2-22-2-222222-2-222-22-2-2-2-22000000000000000000000000-22-2200000000
χ3522222-2-2-2-22-2-2-2-222222-2-2-2-222-222000000000000000000000000000000002-22-2
χ3622222-2-2-2-22-2-2-2-222222-2-2-2-222-22200000000000000000000000000000000-22-22
χ3722222-2-2-2-2-22222-2-2-2-2-2-22-2-22-222200000000000000002-2-220000000000000000
χ3822222-2-2-2-2-22222-2-2-2-2-2-22-2-22-22220000000000000000-222-20000000000000000
χ3922222-2-2-2-2-222-2-2-2-2-2222-2-22-222-222-2002-200-2-222000000000000000000000000
χ4022222-2-2-2-2-222-2-2-2-2-2222-2-22-222-22-2200-220022-2-2000000000000000000000000
χ4122222-2-2-2-2-2-2-222-222-2-2-2-222222-2-2000000000000000000000000000000002i−2i−2i2i
χ4222222-2-2-2-2-2-2-222-222-2-2-2-222222-2-200000000000000000000000000000000−2i2i2i−2i
χ4322222-2-2-2-2-2-2-2-2-2-22222222-2-2-222-20000000000000000000000002i−2i−2i2i00000000
χ4422222-2-2-2-2-2-2-2-2-2-22222222-2-2-222-2000000000000000000000000−2i2i2i−2i00000000
χ4544-44-444-4-40004-40004-40000000002200-2-2002-22-2000000000000000000000000
χ4644-44-444-4-40004-40004-4000000000-2-2002200-22-22000000000000000000000000
χ4744-44-444-4-4000-44000-440000000002200-2-200-22-22000000000000000000000000
χ4844-44-444-4-4000-44000-44000000000-2-20022002-22-2000000000000000000000000
χ4944-44-4-4-4440004-4000-440000000002-200-22002-2-22000000000000000000000000
χ5044-44-4-4-4440004-4000-44000000000-22002-200-222-2000000000000000000000000
χ5144-44-4-4-444000-440004-40000000002-200-2200-222-2000000000000000000000000
χ5244-44-4-4-444000-440004-4000000000-22002-2002-2-22000000000000000000000000
χ5344-4-444-44-404-40004-400000000000000000000000004-400000000000000000000
χ5444-4-444-44-404-40004-40000000000000000000000000-4400000000000000000000
χ5544-4-444-44-40-44000-44000000000000000000000004-40000000000000000000000
χ5644-4-444-44-40-44000-4400000000000000000000000-440000000000000000000000
χ5744-4-44-44-4404-4000-44000000000000004000-40000000000000000000000000000
χ5844-4-44-44-4404-4000-4400000000000000-400040000000000000000000000000000
χ5944-4-44-44-440-440004-400000000000004000-400000000000000000000000000000
χ6044-4-44-44-440-440004-40000000000000-4000400000000000000000000000000000
χ61888-8-88-8-880000000000000000000000000000000000000000000000000000000
χ62888-8-8-888-80000000000000000000000000000000000000000000000000000000
χ6316-16000000080000-80000000000000000000000000000000000000000000000000
χ6416-160000000-8000080000000000000000000000000000000000000000000000000

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