Finite Group Databasebeta

← Group #72311152

Character table — Group #72311152

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size11222444444444444448888888816161616161616161616161616161616161632323232323232323232323232323232323232
order1222222222222224444222244444488888888888888884444444444444448888
χ11111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11111-1-1-1-11111
χ5111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ6111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ7111111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-111111111-1-1-1-1-1-1-1-1
χ8111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111
χ9111111111-1-111-1-11-11-111-1-11-1-1-1111111-1-1-1-1iiii−i−i−i−i1-1-111-1-1ii−i−iii−i−ii−ii−i
χ10111111111-1-111-1-11-11-111-1-11-1-1-1111111-1-1-1-1−i−i−i−iiiii1-1-111-1-1−i−iii−i−iii−ii−ii
χ11111111111-1-111-1-11-11-111-1-11-1-1-111-1-1-1-11111iiii−i−i−i−i1-1-1-1-111−i−iiiii−i−i−ii−ii
χ12111111111-1-111-1-11-11-111-1-11-1-1-111-1-1-1-11111−i−i−i−iiiii1-1-1-1-111ii−i−i−i−iiii−ii−i
χ13111111111-1-111-1-11-11-111-1-11-1-1-1-1-11111-1-1-1-1iiii−i−i−i−i-111-1-111−i−iii−i−iiii−ii−i
χ14111111111-1-111-1-11-11-111-1-11-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii-111-1-111ii−i−iii−i−i−ii−ii
χ15111111111-1-111-1-11-11-111-1-11-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i-11111-1-1ii−i−i−i−iii−ii−ii
χ16111111111-1-111-1-11-11-111-1-11-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii-11111-1-1−i−iiiii−i−ii−ii−i
χ1722222222222-2-2-2-2-2-2-2-22-22-2-222-2220000000000000000-22-20000000000000000
χ1822222222222-2-2-2-2-2-2-2-22-22-2-222-2-2-200000000000000002-220000000000000000
χ19222222222-2-2-2-222-22-222-2-22-2-2-22220000000000000000-2-220000000000000000
χ20222222222-2-2-2-222-22-222-2-22-2-2-22-2-2000000000000000022-20000000000000000
χ212222222-2-22222-2-22222-2-2-2-2-22-220022-2-222-2-2000000000000000000000000000
χ222222222-2-22222-2-22222-2-2-2-2-22-2200-2-222-2-222000000000000000000000000000
χ232222222-2-222-2-222-2-2-2-2-22-2222-2-20000000000000000000002i−2i2i−2i000000000000
χ242222222-2-222-2-222-2-2-2-2-22-2222-2-2000000000000000000000−2i2i−2i2i000000000000
χ252222222-2-2-2-222222-22-2-2-222-2-22-20022-2-2-2-222000000000000000000000000000
χ262222222-2-2-2-222222-22-2-2-222-2-22-200-2-22222-2-2000000000000000000000000000
χ272222222-2-2-2-2-2-2-2-2-22-22-222-22-2220000000000000000000002i−2i−2i2i000000000000
χ282222222-2-2-2-2-2-2-2-2-22-22-222-22-222000000000000000000000−2i2i2i−2i000000000000
χ2922222-2-2222222-2-2-2-2-2-2-22-22-2-22200000000000000000000000002i−2i2i−2i00000000
χ3022222-2-2222222-2-2-2-2-2-2-22-22-2-2220000000000000000000000000−2i2i−2i2i00000000
χ3122222-2-22222-2-2222222-2-2-2-22-22-200000000000000000000000000000000022-2-2
χ3222222-2-22222-2-2222222-2-2-2-22-22-2000000000000000000000000000000000-2-222
χ3322222-2-222-2-22222-22-22-222-2-22-2-200000000000000000000000002-2-2200000000
χ3422222-2-222-2-22222-22-22-222-2-22-2-20000000000000000000000000-222-200000000
χ3522222-2-222-2-2-2-2-2-22-22-2-2-22222-220000000000000000000000000000000002i−2i−2i2i
χ3622222-2-222-2-2-2-2-2-22-22-2-2-22222-22000000000000000000000000000000000−2i2i2i−2i
χ3722222-2-2-2-2222222-2-2-2-22-22-22-2-22000000000000000000000000000002i−2i2i−2i0000
χ3822222-2-2-2-2222222-2-2-2-22-22-22-2-2200000000000000000000000000000−2i2i−2i2i0000
χ3922222-2-2-2-222-2-2-2-222222222-2-2-2-2000000000022-2-222-2-20000000000000000000
χ4022222-2-2-2-222-2-2-2-222222222-2-2-2-20000000000-2-222-2-2220000000000000000000
χ4122222-2-2-2-2-2-222-2-2-22-222-2-22222-2000000000000000000000000000002-2-220000
χ4222222-2-2-2-2-2-222-2-2-22-222-2-22222-200000000000000000000000000000-222-20000
χ4322222-2-2-2-2-2-2-2-2222-22-222-2-2-222200000000002i2i−2i−2i−2i−2i2i2i0000000000000000000
χ4422222-2-2-2-2-2-2-2-2222-22-222-2-2-22220000000000−2i−2i2i2i2i2i−2i−2i0000000000000000000
χ45444-4-4004-400004-4040-40000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000000
χ46444-4-4004-400004-4040-4000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000000
χ47444-4-4004-40000-440-4040000000000000000002-22-2-22-220000000000000000000
χ48444-4-4004-40000-440-404000000000000000000-22-222-22-20000000000000000000
χ49444-4-400-4400004-40-4040000000000000000002-2-22-222-20000000000000000000
χ50444-4-400-4400004-40-404000000000000000000-222-22-2-220000000000000000000
χ51444-4-400-440000-44040-40000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000000
χ52444-4-400-440000-44040-4000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000000
χ5344-44-44-400004-40040-4000000000000000004i−4i000000000000000000000000000
χ5444-44-44-400004-40040-400000000000000000−4i4i000000000000000000000000000
χ5544-44-44-40000-4400-4040000000000000004-400000000000000000000000000000
χ5644-44-44-40000-4400-404000000000000000-4400000000000000000000000000000
χ5744-44-4-4400004-400-404000000000004-4000000000000000000000000000000000
χ5844-44-4-4400004-400-40400000000000-44000000000000000000000000000000000
χ5944-44-4-440000-440040-400000000000004i−4i0000000000000000000000000000000
χ6044-44-4-440000-440040-40000000000000−4i4i0000000000000000000000000000000
χ6188-8-8800008-800000000000000000000000000000000000000000000000000000
χ6288-8-880000-8800000000000000000000000000000000000000000000000000000
χ6316-1600000000000000000000000004i−4i00000000000000000000000000000000000
χ6416-160000000000000000000000000−4i4i00000000000000000000000000000000000

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