Finite Group Databasebeta

← Group #150684

Character table — Group #150684

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44
size1111222222444488888888888888881616161616163232323232323232
order12222244444444444444448888888822244488888888
χ111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-1-1-1-1-11-1-11-1-11111-1-1-1-1
χ41111111111111111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-11111
χ511111111111111-11111-1-1-111111111-1-1-1-1-1-1ii−i−iii−i−i
χ611111111111111-11111-1-1-111111111-1-1-1-1-1-1−i−iii−i−iii
χ711111111111111-11111-1-1-1-1-1-1-1-1-1-1-1-111-111ii−i−i−i−iii
χ811111111111111-11111-1-1-1-1-1-1-1-1-1-1-1-111-111−i−iiiii−i−i
χ9111111-1-1-1-1-1-111111-1-11111111-1-1-1-1-111-1-1-11-11-11-11-1
χ10111111-1-1-1-1-1-111111-1-11111111-1-1-1-1-111-1-1-1-11-11-11-11
χ11111111-1-1-1-1-1-111111-1-1111-1-1-1-11111-1-1-1-1111-11-1-11-11
χ12111111-1-1-1-1-1-111111-1-1111-1-1-1-11111-1-1-1-111-11-111-11-1
χ13111111-1-1-1-1-1-111-111-1-1-1-1-11111-1-1-1-11-1-1111i−i−iii−i−ii
χ14111111-1-1-1-1-1-111-111-1-1-1-1-11111-1-1-1-11-1-1111−iii−i−iii−i
χ15111111-1-1-1-1-1-111-111-1-1-1-1-1-1-1-1-111111111-1-1i−i−ii−iii−i
χ16111111-1-1-1-1-1-111-111-1-1-1-1-1-1-1-1-111111111-1-1−iii−ii−i−ii
χ17222222222222222-2-2-2-2-2-2200000000-20020000000000
χ1822222222222222-2-2-2-2-222-200000000200-20000000000
χ19222222-2-2-2-2-2-2222-2-222-2-2200000000200-20000000000
χ20222222-2-2-2-2-2-222-2-2-22222-200000000-20020000000000
χ214444444444-4-4-4-4000000000000000000000000000000
χ22444444-4-4-4-444-4-4000000000000000000000000000000
χ234444-4-444-4-400000000000022-2-222-2-200000000000000
χ244444-4-444-4-4000000000000-2-222-2-22200000000000000
χ254444-4-4-4-44400000000000022-2-2-2-22200000000000000
χ264444-4-4-4-444000000000000-2-22222-2-200000000000000
χ2744-4-400004i−4i000002-22i−2i000002i2−2i222−220000000000000000
χ2844-4-400004i−4i000002-22i−2i00000−2i22i2−22220000000000000000
χ2944-4-400004i−4i00000-22−2i2i0002i2−2i2000022−2200000000000000
χ3044-4-400004i−4i00000-22−2i2i000−2i22i20000−222200000000000000
χ3144-4-40000−4i4i000002-2−2i2i000002i2−2i2−22220000000000000000
χ3244-4-40000−4i4i000002-2−2i2i00000−2i22i222−220000000000000000
χ3344-4-40000−4i4i00000-222i−2i0002i2−2i20000−222200000000000000
χ3444-4-40000−4i4i00000-222i−2i000−2i22i2000022−2200000000000000
χ354-44-44-40000004-4000004i−4i00000000000000000000000
χ364-44-44-40000004-400000−4i4i00000000000000000000000
χ374-44-44-4000000-444000000-40000000000000000000000
χ384-44-44-4000000-44-400000040000000000000000000000
χ394-44-4-4400004i−4i00000000000000000002-202i−2i00000000
χ404-44-4-4400004i−4i0000000000000000000-220−2i2i00000000
χ414-44-4-440000−4i4i00000000000000000002-20−2i2i00000000
χ424-44-4-440000−4i4i0000000000000000000-2202i−2i00000000
χ438-8-88008-8000000000000000000000000000000000000
χ448-8-8800-88000000000000000000000000000000000000

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