Finite Group Databasebeta

← Group #72317524

Character table — Group #72317524

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70
size11112222224444444444448888888816161616161616161616161616161616161616161616161632323232323232323232323232323232
order1244222444222222444444222244442222444444444444888888884444888888888888
χ11111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ6111111111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ9111111111111-1-1-1-111-1-1-1-111-1-111-1-1111-1111-1-1-1-1-111-1-1iiii−i−i−i−iii−i−i11-1-1ii−i−iii−i−i
χ10111111111111-1-1-1-111-1-1-1-111-1-111-1-1111-1111-1-1-1-1-111-1-1−i−i−i−iiiii−i−iii11-1-1−i−iii−i−iii
χ11111111111111-1-1-1-111-1-1-1-111-1-111-1-111-1111-11-1-1-1-1-1-111iiii−i−i−i−i−i−iii-1-111ii−i−i−i−iii
χ12111111111111-1-1-1-111-1-1-1-111-1-111-1-111-1111-11-1-1-1-1-1-111−i−i−i−iiiiiii−i−i-1-111−i−iiiii−i−i
χ13111111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-11-1-1-11-1111111-1-1iiii−i−i−i−i−i−iii-1-111−i−iiiii−i−i
χ14111111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-11-1-1-11-1111111-1-1−i−i−i−iiiiiii−i−i-1-111ii−i−i−i−iii
χ15111111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-11-1-1-111111-1-111iiii−i−i−i−iii−i−i11-1-1−i−iii−i−iii
χ16111111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-11-1-1-111111-1-111−i−i−i−iiiii−i−iii11-1-1ii−i−iii−i−i
χ1722222222222222-2-22222-2-2-2-22-2-2-2-22002-2002-20000-2-222000000000000000000000000
χ1822222222222222-2-22222-2-2-2-22-2-2-2-2200-2200-22000022-2-2000000000000000000000000
χ19222222222222-2-22222-2-222-2-2-22-2-22-2002200220000-2-2-2-2000000000000000000000000
χ20222222222222-2-22222-2-222-2-2-22-2-22-200-2-200-2-200002222000000000000000000000000
χ212222222222-2-22222-2-222222-2-2-22-2-2-2000000000000000000000000000000002-22-20000
χ222222222222-2-22222-2-222222-2-2-22-2-2-200000000000000000000000000000000-22-220000
χ232222222222-2-222-2-2-2-222-2-2-22-22-222-20000000000000000000000002i−2i2i−2i000000000000
χ242222222222-2-222-2-2-2-222-2-2-22-22-222-2000000000000000000000000−2i2i−2i2i000000000000
χ252222222222-2-2-2-222-2-2-2-222-222-2-22-220000000000000000000000002-2-22000000000000
χ262222222222-2-2-2-222-2-2-2-222-222-2-22-22000000000000000000000000-222-2000000000000
χ272222222222-2-2-2-2-2-2-2-2-2-2-2-22-2222-222000000000000000000000000000000002i−2i−2i2i0000
χ282222222222-2-2-2-2-2-2-2-2-2-2-2-22-2222-22200000000000000000000000000000000−2i2i2i−2i0000
χ2922-2-2222-2-2-2222222-2-2-2-2-2-22-22-2-222-200000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ3022-2-2222-2-2-2222222-2-2-2-2-2-22-22-2-222-20000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ3122-2-2222-2-2-22222-2-2-2-2-2-222-22222-2-2-20000000000000000000000000000000000002i−2i2i−2i
χ3222-2-2222-2-2-22222-2-2-2-2-2-222-22222-2-2-2000000000000000000000000000000000000−2i2i−2i2i
χ3322-2-2222-2-2-222-2-222-2-222-2-2-22-2-22-2220000000000000000000000000000000000002-2-22
χ3422-2-2222-2-2-222-2-222-2-222-2-2-22-2-22-222000000000000000000000000000000000000-222-2
χ3522-2-2222-2-2-222-2-2-2-2-2-222222-2-22-22-22000000000000000022-2-2-2-2220000000000000000
χ3622-2-2222-2-2-222-2-2-2-2-2-222222-2-22-22-220000000000000000-2-22222-2-20000000000000000
χ3722-2-2222-2-2-2-2-2222222-2-2-2-222-22-2-2-222-2002-20022-2-20000000000000000000000000000
χ3822-2-2222-2-2-2-2-2222222-2-2-2-222-22-2-2-22-2200-2200-2-2220000000000000000000000000000
χ3922-2-2222-2-2-2-2-222-2-222-2-222-2-2-2-2222200000000000000000000000000002-22-200000000
χ4022-2-2222-2-2-2-2-222-2-222-2-222-2-2-2-222220000000000000000000000000000-22-2200000000
χ4122-2-2222-2-2-2-2-2-2-2222222-2-2-2-22222-2-200000000000000000000000000002-2-2200000000
χ4222-2-2222-2-2-2-2-2-2-2222222-2-2-2-22222-2-20000000000000000000000000000-222-200000000
χ4322-2-2222-2-2-2-2-2-2-2-2-2222222222-2-2-22-22-2002-200-2-2220000000000000000000000000000
χ4422-2-2222-2-2-2-2-2-2-2-2-2222222222-2-2-22-2-2200-220022-2-20000000000000000000000000000
χ454444-44-44-4-400004-400004-4000000002-200-22002-22-20000000000000000000000000000
χ464444-44-44-4-400004-400004-400000000-22002-200-22-220000000000000000000000000000
χ474444-44-44-4-40000-440000-44000000002-200-2200-22-220000000000000000000000000000
χ484444-44-44-4-40000-440000-4400000000-22002-2002-22-20000000000000000000000000000
χ494444-4-44-44-44-400004-4000000000000000000000000004-4000000000000000000000000
χ504444-4-44-44-44-400004-400000000000000000000000000-44000000000000000000000000
χ514444-4-44-44-4-440000-440000000000000000000000004-400000000000000000000000000
χ524444-4-44-44-4-440000-44000000000000000000000000-4400000000000000000000000000
χ5344-4-4-44-4-44400004-40000-44000000002200-2-2002-2-220000000000000000000000000000
χ5444-4-4-44-4-44400004-40000-4400000000-2-2002200-222-20000000000000000000000000000
χ5544-4-4-44-4-4440000-4400004-4000000002200-2-200-222-20000000000000000000000000000
χ5644-4-4-44-4-4440000-4400004-400000000-2-20022002-2-220000000000000000000000000000
χ5744-4-4-4-444-444-40000-44000000000000004000-4000000000000000000000000000000000
χ5844-4-4-4-444-444-40000-4400000000000000-40004000000000000000000000000000000000
χ5944-4-4-4-444-44-4400004-40000000000000004000-400000000000000000000000000000000
χ6044-4-4-4-444-44-4400004-4000000000000000-4000400000000000000000000000000000000
χ6188888-8-8-8-88000000000000000000000000000000000000000000000000000000000000
χ6288-8-88-8-888-8000000000000000000000000000000000000000000000000000000000000
χ638-88i−8i000000004-400004i−4i000000000000000000000000002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ30000000000000000
χ648-88i−8i000000004-400004i−4i00000000000000000000000000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ30000000000000000
χ658-88i−8i00000000-440000−4i4i000000000000000000000000002ζ3−2ζ3−2ζ2ζ−2ζ32ζ32ζ−2ζ0000000000000000
χ668-88i−8i00000000-440000−4i4i00000000000000000000000000−2ζ32ζ32ζ−2ζ2ζ3−2ζ3−2ζ2ζ0000000000000000
χ678-8−8i8i000000004-40000−4i4i000000000000000000000000002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ0000000000000000
χ688-8−8i8i000000004-40000−4i4i00000000000000000000000000−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ0000000000000000
χ698-8−8i8i00000000-4400004i−4i000000000000000000000000002ζ−2ζ−2ζ32ζ3−2ζ2ζ2ζ3−2ζ30000000000000000
χ708-8−8i8i00000000-4400004i−4i00000000000000000000000000−2ζ2ζ2ζ3−2ζ32ζ−2ζ−2ζ32ζ30000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.