Finite Group Databasebeta

← Group #72258321

Character table — Group #72258321

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76
size111122222244444444444444448888881616161616161616161616161616161616161616161616161616161616161616323232323232323232323232
order1244222444222222224444444422244422224444444444444444444488888888444488888888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111-1-111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ91111111111111111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-1-1-11111ii−i−iii−i−iii−i−i
χ101111111111111111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-1-1-11111−i−iii−i−iii−i−iii
χ111111111111111111-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111iiii−i−i−i−i1111-1-1-1-1ii−i−i−i−iii−i−iii
χ121111111111111111-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111−i−i−i−iiiii1111-1-1-1-1−i−iiiii−i−iii−i−i
χ131111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1−i−iiiii−i−i−i−iii
χ141111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1ii−i−i−i−iiiii−i−i
χ151111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiii−i−i−i−i-1-1-1-11111−i−iii−i−iiiii−i−i
χ161111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−iiiii-1-1-1-11111ii−i−iii−i−i−i−iii
χ17222222222222-2-2-2-22222-2-2-2-2222-2-2-22-200000000000000000000000022-2-222-2-2000000000000
χ18222222222222-2-2-2-22222-2-2-2-2222-2-2-22-2000000000000000000000000-2-222-2-222000000000000
χ19222222222222-2-2-2-2-2-222-2-2-2-2-2-2-2222-2200000000000000000000000022-2-2-2-222000000000000
χ20222222222222-2-2-2-2-2-222-2-2-2-2-2-2-2222-22000000000000000000000000-2-22222-2-2000000000000
χ212222222222-2-222-2-222-2-222-2-222-22-2-2-22002-2002-2000022-2-20000000000000000000000000000
χ222222222222-2-222-2-222-2-222-2-222-22-2-2-2200-2200-220000-2-2220000000000000000000000000000
χ232222222222-2-222-2-2-2-2-2-222-2-2-2-22-2222-2002-2002-20000-2-2220000000000000000000000000000
χ242222222222-2-222-2-2-2-2-2-222-2-2-2-22-2222-200-2200-22000022-2-20000000000000000000000000000
χ252222222222-2-2-2-22222-2-2-2-22222-2-222-2-22-2002-20022-2-200000000000000000000000000000000
χ262222222222-2-2-2-22222-2-2-2-22222-2-222-2-2-2200-2200-2-22200000000000000000000000000000000
χ272222222222-2-2-2-222-2-2-2-2-2-222-2-222-2-2222-2002-200-2-22200000000000000000000000000000000
χ282222222222-2-2-2-222-2-2-2-2-2-222-2-222-2-222-2200-220022-2-200000000000000000000000000000000
χ2922-2-2222-2-2-22222-2-222-2-2-2-222-2-222-22-2-200000000000000000000000000000000000000002i−2i2i−2i
χ3022-2-2222-2-2-22222-2-222-2-2-2-222-2-222-22-2-20000000000000000000000000000000000000000−2i2i−2i2i
χ3122-2-2222-2-2-22222-2-2-2-2-2-2-2-22222-2-22-22200000000000000000000000000000000000000002-2-22
χ3222-2-2222-2-2-22222-2-2-2-2-2-2-2-22222-2-22-2220000000000000000000000000000000000000000-222-2
χ3322-2-2222-2-2-222-2-22222-2-222-2-2-2-22-22-2-22000000000000000022-2-222-2-200000000000000000000
χ3422-2-2222-2-2-222-2-22222-2-222-2-2-2-22-22-2-220000000000000000-2-222-2-22200000000000000000000
χ3522-2-2222-2-2-222-2-222-2-2-2-222-2-222-22-222-200000000000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ3622-2-2222-2-2-222-2-222-2-2-2-222-2-222-22-222-20000000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ3722-2-2222-2-2-2-2-222222222-2-2-2-2-2-2-222-22-2000000000000000000000000000000002-22-200000000
χ3822-2-2222-2-2-2-2-222222222-2-2-2-2-2-2-222-22-200000000000000000000000000000000-22-2200000000
χ3922-2-2222-2-2-2-2-22222-2-222-2-2-2-2222-2-22-22000000000000000000000000000000002i−2i−2i2i00000000
χ4022-2-2222-2-2-2-2-22222-2-222-2-2-2-2222-2-22-2200000000000000000000000000000000−2i2i2i−2i00000000
χ4122-2-2222-2-2-2-2-2-2-2-2-222222222-2-2-2-2-22220000000000000000000000000000000000002-22-20000
χ4222-2-2222-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2222000000000000000000000000000000000000-22-220000
χ4322-2-2222-2-2-2-2-2-2-2-2-2-2-222222222222-2-2-20000000000000000000000000000000000002i−2i−2i2i0000
χ4422-2-2222-2-2-2-2-2-2-2-2-2-2-222222222222-2-2-2000000000000000000000000000000000000−2i2i2i−2i0000
χ4544444-4-4-4-444-40000004-40000000000000000000000000000000000000000004-4000000000000
χ4644444-4-4-4-444-40000004-4000000000000000000000000000000000000000000-44000000000000
χ4744444-4-4-4-44-44000000-4400000000000000000000000000000000000000004-400000000000000
χ4844444-4-4-4-44-44000000-440000000000000000000000000000000000000000-4400000000000000
χ494444-44-44-4-400004-40000004-40000000000000000004-400000000000000000000000000000000
χ504444-44-44-4-400004-40000004-4000000000000000000-4400000000000000000000000000000000
χ514444-44-44-4-40000-44000000-4400000000000000004-40000000000000000000000000000000000
χ524444-44-44-4-40000-44000000-440000000000000000-440000000000000000000000000000000000
χ534444-4-44-44-4004-40000004-40000000000000000000000004-40000000000000000000000000000
χ544444-4-44-44-4004-40000004-4000000000000000000000000-440000000000000000000000000000
χ554444-4-44-44-400-44000000-4400000000000000000000004-4000000000000000000000000000000
χ564444-4-44-44-400-44000000-440000000000000000000000-44000000000000000000000000000000
χ5744-4-44-4-444-44-4000000-44000000000000000000000000000000000000004i−4i0000000000000000
χ5844-4-44-4-444-44-4000000-4400000000000000000000000000000000000000−4i4i0000000000000000
χ5944-4-44-4-444-4-440000004-40000000000000000000000000000000000004i−4i000000000000000000
χ6044-4-44-4-444-4-440000004-4000000000000000000000000000000000000−4i4i000000000000000000
χ6144-4-4-44-4-44400004-4000000-440000000004000-400000000000000000000000000000000000000
χ6244-4-4-44-4-44400004-4000000-44000000000-4000400000000000000000000000000000000000000
χ6344-4-4-44-4-4440000-440000004-4000000004000-4000000000000000000000000000000000000000
χ6444-4-4-44-4-4440000-440000004-400000000-40004000000000000000000000000000000000000000
χ6544-4-4-4-444-44004-4000000-440000000000004000-40000000000000000000000000000000000000
χ6644-4-4-4-444-44004-4000000-44000000000000-400040000000000000000000000000000000000000
χ6744-4-4-4-444-4400-440000004-400000000000004000-4000000000000000000000000000000000000
χ6844-4-4-4-444-4400-440000004-40000000000000-40004000000000000000000000000000000000000
χ698-88i−8i0000000000004-40000004i−4i00000000000000000000002-22i−2i2-22i−2i00000000000000000000
χ708-88i−8i0000000000004-40000004i−4i0000000000000000000000-22−2i2i-22−2i2i00000000000000000000
χ718-88i−8i000000000000-44000000−4i4i00000000000000000000002i−2i-22−2i2i2-200000000000000000000
χ728-88i−8i000000000000-44000000−4i4i0000000000000000000000−2i2i2-22i−2i-2200000000000000000000
χ738-8−8i8i0000000000004-4000000−4i4i00000000000000000000002-2−2i2i2-2−2i2i00000000000000000000
χ748-8−8i8i0000000000004-4000000−4i4i0000000000000000000000-222i−2i-222i−2i00000000000000000000
χ758-8−8i8i000000000000-440000004i−4i00000000000000000000002i−2i2-2−2i2i-2200000000000000000000
χ768-8−8i8i000000000000-440000004i−4i0000000000000000000000−2i2i-222i−2i2-200000000000000000000

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