Finite Group Databasebeta

← Group #128396

Character table — Group #128396

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222224444444444444444444444444444444488888888888816161616161616161616161616161616
order12222222222244444444222244444444444444444444444444444444444444448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i
χ9111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-1
χ10111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-111
χ11111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ12111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ13111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ14111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1
χ15111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1−i−iiiii−i−iii−i−i−i−iii
χ1711-11-1-11-11-11-1iiii−i−i−i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i11-1-111-1-1i−ii−i11-1-1ii−i−i1-1i−i1-1i−i1-1i−i1-1i−i
χ1811-11-1-11-11-11-1iiii−i−i−i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i11-1-111-1-1i−ii−i11-1-1ii−i−i-11−ii-11−ii-11−ii-11−ii
χ1911-11-1-11-11-11-1iiii−i−i−i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i-1-111-1-111−ii−ii-1-111−i−iiii−i-11i−i-11−ii1-1−ii1-1
χ2011-11-1-11-11-11-1iiii−i−i−i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i-1-111-1-111−ii−ii-1-111−i−iii−ii1-1−ii1-1i−i-11i−i-11
χ2111-11-1-11-11-11-1iiii−i−i−i−i11-1-1ii−i−i-1-1-1-11111−i−i−i−iiiii11-1-111-1-1i−ii−i-1-111−i−iii1-1i−i-11−ii1-1i−i-11−ii
χ2211-11-1-11-11-11-1iiii−i−i−i−i11-1-1ii−i−i-1-1-1-11111−i−i−i−iiiii11-1-111-1-1i−ii−i-1-111−i−iii-11−ii1-1i−i-11−ii1-1i−i
χ2311-11-1-11-11-11-1iiii−i−i−i−i11-1-1ii−i−i-1-1-1-11111−i−i−i−iiiii-1-111-1-111−ii−ii11-1-1ii−i−ii−i-11−ii1-1−ii1-1i−i-11
χ2411-11-1-11-11-11-1iiii−i−i−i−i11-1-1ii−i−i-1-1-1-11111−i−i−i−iiiii-1-111-1-111−ii−ii11-1-1ii−i−i−ii1-1i−i-11i−i-11−ii1-1
χ2511-11-1-11-11-11-1−i−i−i−iiiii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii11-1-111-1-1−ii−ii11-1-1−i−iii1-1−ii1-1−ii1-1−ii1-1−ii
χ2611-11-1-11-11-11-1−i−i−i−iiiii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii11-1-111-1-1−ii−ii11-1-1−i−iii-11i−i-11i−i-11i−i-11i−i
χ2711-11-1-11-11-11-1−i−i−i−iiiii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii-1-111-1-111i−ii−i-1-111ii−i−ii−i1-1i−i1-1−ii-11−ii-11
χ2811-11-1-11-11-11-1−i−i−i−iiiii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii-1-111-1-111i−ii−i-1-111ii−i−i−ii-11−ii-11i−i1-1i−i1-1
χ2911-11-1-11-11-11-1−i−i−i−iiiii11-1-1−i−iii-1-1-1-11111iiii−i−i−i−i11-1-111-1-1−ii−ii-1-111ii−i−i1-1−ii-11i−i1-1−ii-11i−i
χ3011-11-1-11-11-11-1−i−i−i−iiiii11-1-1−i−iii-1-1-1-11111iiii−i−i−i−i11-1-111-1-1−ii−ii-1-111ii−i−i-11i−i1-1−ii-11i−i1-1−ii
χ3111-11-1-11-11-11-1−i−i−i−iiiii11-1-1−i−iii-1-1-1-11111iiii−i−i−i−i-1-111-1-111i−ii−i11-1-1−i−iiii−i1-1−ii-11−ii-11i−i1-1
χ3211-11-1-11-11-11-1−i−i−i−iiiii11-1-1−i−iii-1-1-1-11111iiii−i−i−i−i-1-111-1-111i−ii−i11-1-1−i−iii−ii-11i−i1-1i−i1-1−ii-11
χ3322222222222222222222-2-2-2-2-2-2-2-200000000000000002222-2-2-2-222-2-2000000000000000000000000
χ3422222222222222222222-2-2-2-2-2-2-2-20000000000000000-2-2-2-22222-2-222000000000000000000000000
χ35222222222222-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000002222-2-2-2-2-2-222000000000000000000000000
χ36222222222222-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000-2-2-2-2222222-2-2000000000000000000000000
χ37222-2-22-2-2-2-222000000002-22-20000000000002i2i−2i−2i2i2i−2i−2i2i−2i2i−2i2i−2i2i−2i000000002-22-20000000000000000
χ38222-2-22-2-2-2-222000000002-22-20000000000002i2i−2i−2i2i2i−2i−2i−2i2i−2i2i−2i2i−2i2i00000000-22-220000000000000000
χ39222-2-22-2-2-2-222000000002-22-2000000000000−2i−2i2i2i−2i−2i2i2i2i−2i2i−2i2i−2i2i−2i00000000-22-220000000000000000
χ40222-2-22-2-2-2-222000000002-22-2000000000000−2i−2i2i2i−2i−2i2i2i−2i2i−2i2i−2i2i−2i2i000000002-22-20000000000000000
χ41222-2-22-2-2-2-22200000000-22-2200002i2i−2i−2i2i2i−2i−2i000000002i−2i2i−2i−2i2i−2i2i00002-22-200000000000000000000
χ42222-2-22-2-2-2-22200000000-22-2200002i2i−2i−2i2i2i−2i−2i00000000−2i2i−2i2i2i−2i2i−2i0000-22-2200000000000000000000
χ43222-2-22-2-2-2-22200000000-22-220000−2i−2i2i2i−2i−2i2i2i000000002i−2i2i−2i−2i2i−2i2i0000-22-2200000000000000000000
χ44222-2-22-2-2-2-22200000000-22-220000−2i−2i2i2i−2i−2i2i2i00000000−2i2i−2i2i2i−2i2i−2i00002-22-200000000000000000000
χ4522-22-2-22-22-22-22i2i2i2i−2i−2i−2i−2i-2-222−2i−2i2i2i000000000000000022-2-2-2-2222i−2i−2i2i000000000000000000000000
χ4622-22-2-22-22-22-22i2i2i2i−2i−2i−2i−2i-2-222−2i−2i2i2i0000000000000000-2-22222-2-2−2i2i2i−2i000000000000000000000000
χ4722-22-2-22-22-22-2−2i−2i−2i−2i2i2i2i2i-2-2222i2i−2i−2i000000000000000022-2-2-2-222−2i2i2i−2i000000000000000000000000
χ4822-22-2-22-22-22-2−2i−2i−2i−2i2i2i2i2i-2-2222i2i−2i−2i0000000000000000-2-22222-2-22i−2i−2i2i000000000000000000000000
χ4922-2-22-2-22-222-2000000002-2-2200000000000022-2-2-2-2222i−2i−2i2i2i−2i−2i2i00000000−2i2i2i−2i0000000000000000
χ5022-2-22-2-22-222-2000000002-2-2200000000000022-2-2-2-222−2i2i2i−2i−2i2i2i−2i000000002i−2i−2i2i0000000000000000
χ5122-2-22-2-22-222-2000000002-2-22000000000000-2-22222-2-22i−2i−2i2i2i−2i−2i2i000000002i−2i−2i2i0000000000000000
χ5222-2-22-2-22-222-2000000002-2-22000000000000-2-22222-2-2−2i2i2i−2i−2i2i2i−2i00000000−2i2i2i−2i0000000000000000
χ5322-2-22-2-22-222-200000000-222-200002i2i−2i−2i−2i−2i2i2i000000002i−2i−2i2i−2i2i2i−2i00002-2-2200000000000000000000
χ5422-2-22-2-22-222-200000000-222-200002i2i−2i−2i−2i−2i2i2i00000000−2i2i2i−2i2i−2i−2i2i0000-222-200000000000000000000
χ5522-2-22-2-22-222-200000000-222-20000−2i−2i2i2i2i2i−2i−2i000000002i−2i−2i2i−2i2i2i−2i0000-222-200000000000000000000
χ5622-2-22-2-22-222-200000000-222-20000−2i−2i2i2i2i2i−2i−2i00000000−2i2i2i−2i2i−2i−2i2i00002-2-2200000000000000000000
χ5744444444-4-4-4-444-4-444-4-4000000000000000000000000000000000000000000000000000000000000
χ5844444444-4-4-4-4-4-444-4-444000000000000000000000000000000000000000000000000000000000000
χ59444-4-44-4-444-4-40000000000004-44-40000000000000000000000000000000000000000000000000000
χ60444-4-44-4-444-4-4000000000000-44-440000000000000000000000000000000000000000000000000000
χ6144-44-4-44-4-44-444i4i−4i−4i−4i−4i4i4i000000000000000000000000000000000000000000000000000000000000
χ6244-44-4-44-4-44-44−4i−4i4i4i4i4i−4i−4i000000000000000000000000000000000000000000000000000000000000
χ6344-4-44-4-444-4-440000000000004i−4i−4i4i0000000000000000000000000000000000000000000000000000
χ6444-4-44-4-444-4-44000000000000−4i4i4i−4i0000000000000000000000000000000000000000000000000000
χ654-444-4-4-440000004i−4i004i−4i000000002i−2i2i−2i2i−2i2i−2i2-22-22-22-2000000000000000000000000000000000000
χ664-444-4-4-440000004i−4i004i−4i00000000−2i2i−2i2i−2i2i−2i2i-22-22-22-22000000000000000000000000000000000000
χ674-444-4-4-44000000−4i4i00−4i4i000000002i−2i2i−2i2i−2i2i−2i-22-22-22-22000000000000000000000000000000000000
χ684-444-4-4-44000000−4i4i00−4i4i00000000−2i2i−2i2i−2i2i−2i2i2-22-22-22-2000000000000000000000000000000000000
χ694-44-44-44-400004i−4i004i−4i00000000002-2-222-2-222i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000
χ704-44-44-44-400004i−4i004i−4i0000000000-222-2-222-2−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000
χ714-44-44-44-40000−4i4i00−4i4i00000000002-2-222-2-22−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000
χ724-44-44-44-40000−4i4i00−4i4i0000000000-222-2-222-22i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000
χ734-4-4444-4-40000004-400-44000000002i−2i2i−2i−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000
χ744-4-4444-4-40000004-400-4400000000−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000
χ754-4-4444-4-4000000-44004-4000000002i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000
χ764-4-4444-4-4000000-44004-400000000−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000
χ774-4-4-4-444400004-400-4400000000002-2-22-222-22-2-22-222-2000000000000000000000000000000000000
χ784-4-4-4-444400004-400-440000000000-222-22-2-22-222-22-2-22000000000000000000000000000000000000
χ794-4-4-4-44440000-44004-400000000002-2-22-222-2-222-22-2-22000000000000000000000000000000000000
χ804-4-4-4-44440000-44004-40000000000-222-22-2-222-2-22-222-2000000000000000000000000000000000000

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