Finite Group Databasebeta

← Group #72319369

Character table — Group #72319369

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76
size11222222244444444448888888888888888816161616161616161616161616161616161616161616161616161616323232323232323232323232
order1222222224444444444222222224444444444444444444444444444488888888244444444444
χ11111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1iiii−i−i−i−i
χ61111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-11111−i−i−i−iiiii
χ71111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1−i−i−i−iiiii
χ81111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-11111iiii−i−i−i−i
χ91111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ101111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-1-111
χ111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-111
χ121111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-1
χ131111111111111-1-1-1-111-1-1-1-1-1-1-1-1111-1-11111-1-111iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-111ii−i−i−i−iii
χ141111111111111-1-1-1-111-1-1-1-1-1-1-1-1111-1-11111-1-111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-1111111-1-1−i−iiiii−i−i
χ151111111111111-1-1-1-111-1-1-1-1-1-1-1-1111-1-11111-1-111−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-111−i−iiiii−i−i
χ161111111111111-1-1-1-111-1-1-1-1-1-1-1-1111-1-11111-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-1111111-1-1ii−i−i−i−iii
χ171111-11-1-1-11-111ii−i−i1-111-1-111-1-11-1-1i−iii−i−ii−ii−i11-1-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i1-1i−i1-1i−i1-1i−i
χ181111-11-1-1-11-111ii−i−i1-111-1-111-1-11-1-1i−iii−i−ii−ii−i11-1-1ii−i−i11-1-1ii−i−i-1-111−i−iii-11−ii-11−ii-11−ii
χ191111-11-1-1-11-111ii−i−i1-111-1-111-1-11-1-1i−iii−i−ii−ii−i-1-111−i−iii-1-111−i−iii11-1-1ii−i−i1-1i−i-11−ii-11−ii
χ201111-11-1-1-11-111ii−i−i1-111-1-111-1-11-1-1i−iii−i−ii−ii−i-1-111−i−iii-1-111−i−iii-1-111−i−iii-11−ii1-1i−i1-1i−i
χ211111-11-1-1-11-111ii−i−i1-1-1-111-1-1111-1-1i−i−i−iiii−i−iiii−i−i-1-111−i−iii11-1-111-1-1ii−i−i-11−iii−i-11−ii1-1
χ221111-11-1-1-11-111ii−i−i1-1-1-111-1-1111-1-1i−i−i−iiii−i−iiii−i−i-1-111−i−iii11-1-1-1-111−i−iii1-1i−i−ii1-1i−i-11
χ231111-11-1-1-11-111ii−i−i1-1-1-111-1-1111-1-1i−i−i−iiii−i−ii−i−iii11-1-1ii−i−i-1-11111-1-1ii−i−i-11−ii−ii1-1i−i-11
χ241111-11-1-1-11-111ii−i−i1-1-1-111-1-1111-1-1i−i−i−iiii−i−ii−i−iii11-1-1ii−i−i-1-111-1-111−i−iii1-1i−ii−i-11−ii1-1
χ251111-11-1-1-11-111−i−iii1-111-1-111-1-11-1-1−ii−i−iii−ii−ii11-1-1−i−iii11-1-1−i−iii11-1-1−i−iii1-1−ii1-1−ii1-1−ii
χ261111-11-1-1-11-111−i−iii1-111-1-111-1-11-1-1−ii−i−iii−ii−ii11-1-1−i−iii11-1-1−i−iii-1-111ii−i−i-11i−i-11i−i-11i−i
χ271111-11-1-1-11-111−i−iii1-111-1-111-1-11-1-1−ii−i−iii−ii−ii-1-111ii−i−i-1-111ii−i−i11-1-1−i−iii1-1−ii-11i−i-11i−i
χ281111-11-1-1-11-111−i−iii1-111-1-111-1-11-1-1−ii−i−iii−ii−ii-1-111ii−i−i-1-111ii−i−i-1-111ii−i−i-11i−i1-1−ii1-1−ii
χ291111-11-1-1-11-111−i−iii1-1-1-111-1-1111-1-1−iiii−i−i−iii−iii−i−i11-1-1−i−iii-1-11111-1-1−i−iii-11i−ii−i1-1−ii-11
χ301111-11-1-1-11-111−i−iii1-1-1-111-1-1111-1-1−iiii−i−i−iii−iii−i−i11-1-1−i−iii-1-111-1-111ii−i−i1-1−ii−ii-11i−i1-1
χ311111-11-1-1-11-111−i−iii1-1-1-111-1-1111-1-1−iiii−i−i−iii−i−i−iii-1-111ii−i−i11-1-111-1-1−i−iii-11i−i−ii-11i−i1-1
χ321111-11-1-1-11-111−i−iii1-1-1-111-1-1111-1-1−iiii−i−i−iii−i−i−iii-1-111ii−i−i11-1-1-1-111ii−i−i1-1−iii−i1-1−ii-11
χ3322222222222-2-22222222-22-22-22-2-2-2-2222222-2-2-2-2000000000000000000000000000000000000
χ3422222222222-2-2222222-22-22-22-22-2-2-222-2-2-2-2-2-222000000000000000000000000000000000000
χ3522222222222-2-2-2-2-2-2222-22-22-22-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000000000
χ3622222222222-2-2-2-2-2-222-22-22-22-22-2-2-2-2-2222222-2-2000000000000000000000000000000000000
χ372222-22-2-2-22-2-2-22i2i−2i−2i2-22-2-222-2-22-2222i−2i2i2i−2i−2i−2i2i−2i2i000000000000000000000000000000000000
χ382222-22-2-2-22-2-2-22i2i−2i−2i2-2-222-2-222-2-2222i−2i−2i−2i2i2i−2i2i2i−2i000000000000000000000000000000000000
χ392222-22-2-2-22-2-2-2−2i−2i2i2i2-22-2-222-2-22-222−2i2i−2i−2i2i2i2i−2i2i−2i000000000000000000000000000000000000
χ402222-22-2-2-22-2-2-2−2i−2i2i2i2-2-222-2-222-2-222−2i2i2i2i−2i−2i2i−2i−2i2i000000000000000000000000000000000000
χ4122-2-222-22-2-2-22200002222-22-2-22-2-22-200000000002i−2i2i−2i00002i−2i2i−2i000000000000000000000000
χ4222-2-222-22-2-2-22200002222-22-2-22-2-22-20000000000−2i2i−2i2i0000−2i2i−2i2i000000000000000000000000
χ4322-2-222-22-2-2-222000022-2-22-222-22-22-200000000002-22-20000-22-22000000000000000000000000
χ4422-2-222-22-2-2-222000022-2-22-222-22-22-20000000000-22-2200002-22-2000000000000000000000000
χ4522-2-222-22-2-2-2-2-20000222-2-2-2-22222-22000000000000002-22-200002-22-200000000000000000000
χ4622-2-222-22-2-2-2-2-20000222-2-2-2-22222-2200000000000000-22-220000-22-2200000000000000000000
χ4722-2-222-22-2-2-2-2-2000022-22222-2-2-22-22000000000000002i−2i2i−2i0000−2i2i−2i2i00000000000000000000
χ4822-2-222-22-2-2-2-2-2000022-22222-2-2-22-2200000000000000−2i2i−2i2i00002i−2i2i−2i00000000000000000000
χ4922-2-2-222-22-222200002-2222-2-2-2-22-2-2200000000002i−2i−2i2i00002i−2i−2i2i000000000000000000000000
χ5022-2-2-222-22-222200002-2222-2-2-2-22-2-220000000000−2i2i2i−2i0000−2i2i2i−2i000000000000000000000000
χ5122-2-2-222-22-222200002-2-2-2-22222-2-2-2200000000002-2-220000-222-2000000000000000000000000
χ5222-2-2-222-22-222200002-2-2-2-22222-2-2-220000000000-222-200002-2-22000000000000000000000000
χ5322-2-2-222-22-22-2-200002-22-222-22-2-222-2000000000000002i−2i−2i2i00002i−2i−2i2i00000000000000000000
χ5422-2-2-222-22-22-2-200002-22-222-22-2-222-200000000000000−2i2i2i−2i0000−2i2i2i−2i00000000000000000000
χ5522-2-2-222-22-22-2-200002-2-22-2-22-22222-2000000000000002-2-220000-222-200000000000000000000
χ5622-2-2-222-22-22-2-200002-2-22-2-22-22222-200000000000000-222-200002-2-2200000000000000000000
χ57444444444-4-4004444-4-400000000000-4-400000000000000000000000000000000000000000000
χ58444444444-4-400-4-4-4-4-4-4000000000004400000000000000000000000000000000000000000000
χ594444-44-4-4-4-44004i4i−4i−4i-4400000000000−4i4i00000000000000000000000000000000000000000000
χ604444-44-4-4-4-4400−4i−4i4i4i-44000000000004i−4i00000000000000000000000000000000000000000000
χ61444-44-44-4-400004i−4i4i−4i0000000000000000000000000000000000000002-22-22i−2i2i−2i000000000000
χ62444-44-44-4-400004i−4i4i−4i000000000000000000000000000000000000000-22-22−2i2i−2i2i000000000000
χ63444-44-44-4-40000−4i4i−4i4i0000000000000000000000000000000000000002-22-2−2i2i−2i2i000000000000
χ64444-44-44-4-40000−4i4i−4i4i000000000000000000000000000000000000000-22-222i−2i2i−2i000000000000
χ65444-4-4-4-44400004-4-440000000000000000000000000000000000000002-2-222-2-22000000000000
χ66444-4-4-4-44400004-4-44000000000000000000000000000000000000000-222-2-222-2000000000000
χ67444-4-4-4-4440000-444-40000000000000000000000000000000000000002-2-22-222-2000000000000
χ68444-4-4-4-4440000-444-4000000000000000000000000000000000000000-222-22-2-22000000000000
χ6944-4-444-44-444000000-4-400000000000004i−4i4i−4i0000000000000000000000000000000000000000
χ7044-4-444-44-444000000-4-40000000000000−4i4i−4i4i0000000000000000000000000000000000000000
χ7144-4-4-444-444-4000000-4400000000000004-4-440000000000000000000000000000000000000000
χ7244-4-4-444-444-4000000-440000000000000-444-40000000000000000000000000000000000000000
χ7388-888-8-8-880000000000000000000000000000000000000000000000000000000000000000000
χ7488-88-8-888-80000000000000000000000000000000000000000000000000000000000000000000
χ7516-160000000008-8000000000000000000000000000000000000000000000000000000000000000
χ7616-16000000000-88000000000000000000000000000000000000000000000000000000000000000

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