Finite Group Databasebeta

← Group #72234058

Character table — Group #72234058

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76
size1111222222222244444444448888888888888888161616161616161616161616161616161616161632323232323232323232323232323232
order1222222222444422224444442244444444444444222244444444888888884444444488888888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111111-1-1-1-1-1-1-1-1111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111111-1-1-1-1-1-1-1-1111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111
χ71111111111111111111111111111111-1-1-1-1-1-1-1-11-1-111-1-111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111111-1-1-1-1-1-1-1-11-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ91111111111-1-1-1-111-1-111-1-1-1-11-1111-1-11111-1-1-1-1-11111-1-1-1-111-1-1iiii−i−i−i−i1-11-1ii−i−iii−i−iii−i−i
χ101111111111-1-1-1-111-1-111-1-1-1-11-1111-1-11111-1-1-1-1-11111-1-1-1-111-1-1−i−i−i−iiiii1-11-1−i−iii−i−iii−i−iii
χ111111111111-1-1-1-111-1-111-1-1-1-11-1111-1-11111-1-1-1-1-1-1-1-1-1111111-1-1iiii−i−i−i−i-11-11ii−i−i−i−iii−i−iii
χ121111111111-1-1-1-111-1-111-1-1-1-11-1111-1-11111-1-1-1-1-1-1-1-1-1111111-1-1−i−i−i−iiiii-11-11−i−iiiii−i−iii−i−i
χ131111111111-1-1-1-111-1-111-1-1-1-11-1111-1-1-1-1-1-11111-111-1-1-1-111-1-111iiii−i−i−i−i1-1-11−i−iiiii−i−i−i−iii
χ141111111111-1-1-1-111-1-111-1-1-1-11-1111-1-1-1-1-1-11111-111-1-1-1-111-1-111−i−i−i−iiiii1-1-11ii−i−i−i−iiiii−i−i
χ151111111111-1-1-1-111-1-111-1-1-1-11-1111-1-1-1-1-1-11111-1-1-11111-1-1-1-111iiii−i−i−i−i-111-1−i−iii−i−iiiii−i−i
χ161111111111-1-1-1-111-1-111-1-1-1-11-1111-1-1-1-1-1-11111-1-1-11111-1-1-1-111−i−i−i−iiiii-111-1ii−i−iii−i−i−i−iii
χ172222222222222222-2-2-2-222-2-22-2-2-2-22-20000000020022002200000000000000-2-2000000000000
χ182222222222222222-2-2-2-222-2-22-2-2-2-22-200000000200-2-200-2-20000000000000022000000000000
χ1922222222222222-2-2222222-2-2-22-2-22-2-222222222-200000000-2-2-2-2000000000000000000000000
χ2022222222222222-2-2222222-2-2-22-2-22-2-2-2-2-2-2-2-2-2-2-2000000002222000000000000000000000000
χ2122222222222222-2-2-2-2-2-22222-2-222-2-2200000000-222002200000000000000-2-200000000000000
χ2222222222222222-2-2-2-2-2-22222-2-222-2-2200000000-2-2-200-2-2000000000000002200000000000000
χ232222222222-2-2-2-22222-2-2-2-22222-2-2-2-2200000000-2002200-2-200000000000000-22000000000000
χ242222222222-2-2-2-22222-2-2-2-22222-2-2-2-2200000000-200-2-20022000000000000002-2000000000000
χ252222222222-2-2-2-2-2-222-2-2-2-2-2-2-2222-22-20000000022200-2-200000000000000-2200000000000000
χ262222222222-2-2-2-2-2-222-2-2-2-2-2-2-2222-22-2000000002-2-20022000000000000002-200000000000000
χ272222222222-2-2-2-2-2-2-2-222-2-222-2-2-2-22222222-2-2-2-2200000000-2-222000000000000000000000000
χ282222222222-2-2-2-2-2-2-2-222-2-222-2-2-2-2222-2-2-2-2222220000000022-2-2000000000000000000000000
χ2922222-2-2-2-2222-2-22222-2-22-222-2-22-22-2-20000000020000000000000000000000002-22-200000000
χ3022222-2-2-2-2222-2-22222-2-22-222-2-22-22-2-2000000002000000000000000000000000-22-2200000000
χ3122222-2-2-2-2222-2-222-2-2222-2-2-2-22-22-2-2200000000200000000000000000000000000002i−2i2i−2i0000
χ3222222-2-2-2-2222-2-222-2-2222-2-2-2-22-22-2-220000000020000000000000000000000000000−2i2i−2i2i0000
χ3322222-2-2-2-2222-2-2-2-222-2-22-2-2-22-2-2222200000000-20000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ3422222-2-2-2-2222-2-2-2-222-2-22-2-2-22-2-2222200000000-2000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ3522222-2-2-2-2222-2-2-2-2-2-2222-222222-2-22-200000000-2000000000000000000000000000000002i−2i2i−2i
χ3622222-2-2-2-2222-2-2-2-2-2-2222-222222-2-22-200000000-200000000000000000000000000000000−2i2i−2i2i
χ3722222-2-2-2-22-2-222222222-2222-2-2-22-22-200000000-200000000000000000000000000002-2-220000
χ3822222-2-2-2-22-2-222222222-2222-2-2-22-22-200000000-20000000000000000000000000000-222-20000
χ3922222-2-2-2-22-2-22222-2-2-2-2-22-2-2-222-222200000000-20000000000000000000000002i−2i−2i2i00000000
χ4022222-2-2-2-22-2-22222-2-2-2-2-22-2-2-222-222200000000-2000000000000000000000000−2i2i2i−2i00000000
χ4122222-2-2-2-22-2-222-2-22222-22-2-22-22-2-2-22000000002000000000000000000000000000000002-2-22
χ4222222-2-2-2-22-2-222-2-22222-22-2-22-22-2-2-2200000000200000000000000000000000000000000-222-2
χ4322222-2-2-2-22-2-222-2-2-2-2-2-2-222222-222-2-200000000200000000000022-2-2-2-2220000000000000000
χ4422222-2-2-2-22-2-222-2-2-2-2-2-2-222222-222-2-2000000002000000000000-2-22222-2-20000000000000000
χ454444-44-4-44-444-4-4000000-440000000000000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ464444-44-4-44-444-4-4000000-44000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ474444-44-4-44-4-4-4440000004-40000000000000000000000000000002-22-2-22-220000000000000000
χ484444-44-4-44-4-4-4440000004-4000000000000000000000000000000-22-222-22-20000000000000000
χ494444-4-444-4-44444000000-4-40000000000000000000000000000002-2-222-2-220000000000000000
χ504444-4-444-4-44444000000-4-4000000000000000000000000000000-222-2-222-20000000000000000
χ514444-4-444-4-4-4-4-4-4000000440000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ524444-4-444-4-4-4-4-4-400000044000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ5344-4-4004-4004i−4i4i−4i0000000000000000022-2-22i2i−2i−2i02-22-22i−2i2i−2i0000000000000000000000000000
χ5444-4-4004-4004i−4i4i−4i0000000000000000022-2-22i2i−2i−2i0-22-22−2i2i−2i2i0000000000000000000000000000
χ5544-4-4004-4004i−4i4i−4i00000000000000000-2-222−2i−2i2i2i02-2-222i−2i−2i2i0000000000000000000000000000
χ5644-4-4004-4004i−4i4i−4i00000000000000000-2-222−2i−2i2i2i0-222-2−2i2i2i−2i0000000000000000000000000000
χ5744-4-4004-400−4i4i−4i4i0000000000000000022-2-2−2i−2i2i2i02-22-2−2i2i−2i2i0000000000000000000000000000
χ5844-4-4004-400−4i4i−4i4i0000000000000000022-2-2−2i−2i2i2i0-22-222i−2i2i−2i0000000000000000000000000000
χ5944-4-4004-400−4i4i−4i4i00000000000000000-2-2222i2i−2i−2i02-2-22−2i2i2i−2i0000000000000000000000000000
χ6044-4-4004-400−4i4i−4i4i00000000000000000-2-2222i2i−2i−2i0-222-22i−2i−2i2i0000000000000000000000000000
χ614-4-44-40000400004-44-400004-400000002-22-22-22-20000000002-22-2000000000000000000000000
χ624-4-44-40000400004-44-400004-40000000-22-22-22-22000000000-22-22000000000000000000000000
χ634-4-44-40000400004-4-440000-4400000002-22-2-22-220000000002-2-22000000000000000000000000
χ644-4-44-40000400004-4-440000-440000000-22-222-22-2000000000-222-2000000000000000000000000
χ654-4-44-4000040000-444-40000-4400000002-22-22-22-2000000000-22-22000000000000000000000000
χ664-4-44-4000040000-444-40000-440000000-22-22-22-220000000002-22-2000000000000000000000000
χ674-4-44-4000040000-44-4400004-400000002-22-2-22-22000000000-222-2000000000000000000000000
χ684-4-44-4000040000-44-4400004-40000000-22-222-22-20000000002-2-22000000000000000000000000
χ6988-8-800-88008i−8i−8i8i00000000000000000000000000000000000000000000000000000000000000
χ7088-8-800-8800−8i8i8i−8i00000000000000000000000000000000000000000000000000000000000000
χ718-88-80800-8000000000000000000000000004i−4i−4i4i0000000000000000000000000000000000000
χ728-88-80800-800000000000000000000000000−4i4i4i−4i0000000000000000000000000000000000000
χ738-88-80-800800000000000000000000004-4-4400000000000000000000000000000000000000000
χ748-88-80-80080000000000000000000000-444-400000000000000000000000000000000000000000
χ758-8-8880000-8000000008i−8i00000000000000000000000000000000000000000000000000000000
χ768-8-8880000-800000000−8i8i00000000000000000000000000000000000000000000000000000000

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