Finite Group Databasebeta

← Group #495772

Character table — Group #495772

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112222224444444444444444888888888888888888888888888888161616161616161616161616
order12222244442222444444444444222244444444444444444444444444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-1111111-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ711111111111111111111-1-1-1-111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ9111111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-111-1-111-1-1-1-111-1-111-1-111-1-111-1-111-1-111-1-1
χ10111111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1111111-1-111-1-111-1-1-1-111-1-111-1-111
χ11111111-1-1-1-11111-1-1-1-1-1-1111111-1-111-1-111-1-11111-1-1-1-111-1-1-1-111-1-11111-1-1-1-111-1-111
χ12111111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111-1-1111111-1-1-1-111-1-111-1-11111-1-111-1-1
χ13111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-111
χ14111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-11111-1-11111-1-1-1-11111-1-1-1-11111-1-1
χ15111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-111-1-1-1-1-1-111-1-11111-1-1-1-111-1-11111-1-1
χ16111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-111-1-11111-1-111-1-111-1-1-1-111
χ1711-1-11-1ii−i−i11-1-1iii−i−i−i11-1-11-11-11-1i−ii−i1-1i−i1-1ii−i−i1-1i−i1-1i−i1-1i−i1-1i−i1-1i−i1-1i−i
χ1811-1-11-1ii−i−i11-1-1iii−i−i−i11-1-11-11-1-11i−ii−i1-1i−i-11−i−iii1-1i−i1-1i−i1-1i−i-11−ii-11−ii-11−ii
χ1911-1-11-1ii−i−i11-1-1iii−i−i−i11-1-11-1-111-1i−i−ii-11−ii1-1ii−i−i1-1i−i-11−ii-11−ii1-1i−i-11−ii-11−ii
χ2011-1-11-1ii−i−i11-1-1iii−i−i−i11-1-11-1-11-11i−i−ii-11−ii-11−i−iii1-1i−i-11−ii-11−ii-11−ii1-1i−i1-1i−i
χ2111-1-11-1ii−i−i11-1-1iii−i−i−i-1-1111-11-11-1−iii−i-11−ii1-1ii−i−i-11−ii1-1i−i-11−ii-11−ii1-1i−i-11−ii
χ2211-1-11-1ii−i−i11-1-1iii−i−i−i-1-1111-11-1-11−iii−i-11−ii-11−i−iii-11−ii1-1i−i-11−ii1-1i−i-11−ii1-1i−i
χ2311-1-11-1ii−i−i11-1-1iii−i−i−i-1-1111-1-111-1−ii−ii1-1i−i1-1ii−i−i-11−ii-11−ii1-1i−i-11−ii-11−ii1-1i−i
χ2411-1-11-1ii−i−i11-1-1iii−i−i−i-1-1111-1-11-11−ii−ii1-1i−i-11−i−iii-11−ii-11−ii1-1i−i1-1i−i1-1i−i-11−ii
χ2511-1-11-1−i−iii11-1-1−i−i−iiii11-1-11-11-11-1−ii−ii1-1−ii1-1−i−iii1-1−ii1-1−ii1-1−ii1-1−ii1-1−ii1-1−ii
χ2611-1-11-1−i−iii11-1-1−i−i−iiii11-1-11-11-1-11−ii−ii1-1−ii-11ii−i−i1-1−ii1-1−ii1-1−ii-11i−i-11i−i-11i−i
χ2711-1-11-1−i−iii11-1-1−i−i−iiii11-1-11-1-111-1−iii−i-11i−i1-1−i−iii1-1−ii-11i−i-11i−i1-1−ii-11i−i-11i−i
χ2811-1-11-1−i−iii11-1-1−i−i−iiii11-1-11-1-11-11−iii−i-11i−i-11ii−i−i1-1−ii-11i−i-11i−i-11i−i1-1−ii1-1−ii
χ2911-1-11-1−i−iii11-1-1−i−i−iiii-1-1111-11-11-1i−i−ii-11i−i1-1−i−iii-11i−i1-1−ii-11i−i-11i−i1-1−ii-11i−i
χ3011-1-11-1−i−iii11-1-1−i−i−iiii-1-1111-11-1-11i−i−ii-11i−i-11ii−i−i-11i−i1-1−ii-11i−i1-1−ii-11i−i1-1−ii
χ3111-1-11-1−i−iii11-1-1−i−i−iiii-1-1111-1-111-1i−ii−i1-1−ii1-1−i−iii-11i−i-11i−i1-1−ii-11i−i-11i−i1-1−ii
χ3211-1-11-1−i−iii11-1-1−i−i−iiii-1-1111-1-11-11i−ii−i1-1−ii-11ii−i−i-11i−i-11i−i1-1−ii1-1−ii1-1−ii-11i−i
χ3322222222222-22-22-2-22-2-20000-2-22200002200000000000000-2-2-2-20000000000000000
χ3422222222222-22-22-2-22-2-20000-2-2-2-20000-2-20000000000000022220000000000000000
χ352222222222-22-22-22-2-22-22222-2-2000022000000000000-2-2-2-200000000000000000000
χ362222222222-22-22-22-2-22-2-2-2-2-2-2-20000-2-2000000000000222200000000000000000000
χ372222222222-2-2-2-2-2-22-2-2200002200000000222200000000000000-2-2-2-2000000000000
χ382222222222-2-2-2-2-2-22-2-2200002200000000-2-2-2-2000000000000002222000000000000
χ39222222-2-2-2-22-22-2-222-2220000-2-2220000-2-200000000000000-2-2220000000000000000
χ40222222-2-2-2-22-22-2-222-2220000-2-2-2-20000220000000000000022-2-20000000000000000
χ41222222-2-2-2-2-22-222-222-222222-2-20000-2-2000000000000-2-22200000000000000000000
χ42222222-2-2-2-2-22-222-222-22-2-2-2-2-2-200002200000000000022-2-200000000000000000000
χ43222222-2-2-2-2-2-2-2-222-222-20000220000000022-2-200000000000000-2-222000000000000
χ44222222-2-2-2-2-2-2-2-222-222-200002200000000-2-2220000000000000022-2-2000000000000
χ4522-2-22-22i2i−2i−2i2-2-222i−2i−2i−2i2i2i0000-222-200002i−2i00000000000000-22−2i2i0000000000000000
χ4622-2-22-22i2i−2i−2i2-2-222i−2i−2i−2i2i2i0000-22-220000−2i2i000000000000002-22i−2i0000000000000000
χ4722-2-22-22i2i−2i−2i-222-2−2i2i−2i2i−2i2i22-2-2-2200002i−2i000000000000-22−2i2i00000000000000000000
χ4822-2-22-22i2i−2i−2i-222-2−2i2i−2i2i−2i2i-2-222-220000−2i2i0000000000002-22i−2i00000000000000000000
χ4922-2-22-22i2i−2i−2i-2-222−2i−2i2i2i2i−2i00002-2000000002-22i−2i00000000000000-22−2i2i000000000000
χ5022-2-22-22i2i−2i−2i-2-222−2i−2i2i2i2i−2i00002-200000000-22−2i2i000000000000002-22i−2i000000000000
χ5122-2-22-2−2i−2i2i2i2-2-22−2i2i2i2i−2i−2i0000-222-20000−2i2i00000000000000-222i−2i0000000000000000
χ5222-2-22-2−2i−2i2i2i2-2-22−2i2i2i2i−2i−2i0000-22-2200002i−2i000000000000002-2−2i2i0000000000000000
χ5322-2-22-2−2i−2i2i2i-222-22i−2i2i−2i2i−2i22-2-2-220000−2i2i000000000000-222i−2i00000000000000000000
χ5422-2-22-2−2i−2i2i2i-222-22i−2i2i−2i2i−2i-2-222-2200002i−2i0000000000002-2−2i2i00000000000000000000
χ5522-2-22-2−2i−2i2i2i-2-2222i2i−2i−2i−2i2i00002-2000000002-2−2i2i00000000000000-222i−2i000000000000
χ5622-2-22-2−2i−2i2i2i-2-2222i2i−2i−2i−2i2i00002-200000000-222i−2i000000000000002-2−2i2i000000000000
χ574444-4-44-44-40000000000000000002200000000-2-22-22-2000000000000000000000000
χ584444-4-44-44-4000000000000000000-2-20000000022-22-22000000000000000000000000
χ594444-4-4-44-440000000000000000002200000000-2-2-22-22000000000000000000000000
χ604444-4-4-44-44000000000000000000-2-200000000222-22-2000000000000000000000000
χ6144-4-4-444i−4i−4i4i0000000000000000002-200000000-222i−2i−2i2i000000000000000000000000
χ6244-4-4-444i−4i−4i4i000000000000000000-22000000002-2−2i2i2i−2i000000000000000000000000
χ6344-4-4-44−4i4i4i−4i0000000000000000002-200000000-22−2i2i2i−2i000000000000000000000000
χ6444-4-4-44−4i4i4i−4i000000000000000000-22000000002-22i−2i−2i2i000000000000000000000000
χ658-88-800000000000000004i−4i4i−4i00000000000000000000000000000000000000000000
χ668-88-80000000000000000−4i4i−4i4i00000000000000000000000000000000000000000000
χ678-8-8800000000000000004i−4i−4i4i00000000000000000000000000000000000000000000
χ688-8-880000000000000000−4i4i4i−4i00000000000000000000000000000000000000000000

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