Finite Group Databasebeta

← Group #289138

Character table — Group #289138

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111222222224444444448888888881616161616161616161616161616161632323232
order12222244444444488888888888888822244444888888884488
χ111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111
χ61111111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-111-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111
χ9111111111111111-1-1-1-1-1-1-11111-1-1-1-11-1111-1-1-111-1-1-1-1111-11-1
χ10111111111111111-1-1-1-1-1-1-11111-1-1-1-11-1-1-11-11111-1-111-1-1-11-11
χ11111111111111111-1-1-1-1-1-1-11111-1-1-1-1-1111-11-1-1-1-111-1-111-11-11
χ12111111111111111-1-1-1-1-1-1-11111-1-1-1-1-11-1-1-1111-1-11111-1-11-11-1
χ13111111111111111-1-1-1-1-1-1-1-1-1-1-111111-1111-111-1-111-1-1-1-1-111-1
χ14111111111111111-1-1-1-1-1-1-1-1-1-1-111111-1-1-11-1-1-1-1-11111111-1-11
χ15111111111111111-1-1-1-1-1-1-1-1-1-1-11111-1111-111111-1-1-1-1-1-11-1-11
χ16111111111111111-1-1-1-1-1-1-1-1-1-1-11111-11-1-1-11-1-111-1-11111-111-1
χ17222222222-2-22-2-2-222-2-2-2-22000000002-200-2200000000000000
χ18222222222-2-22-2-2-222-2-2-2-2200000000-22002-200000000000000
χ19222222222-2-22-2-2-2-2-22222-2000000002200-2-200000000000000
χ20222222222-2-22-2-2-2-2-22222-200000000-2-2002200000000000000
χ21222222-2-2-2-2-2-22-2200000002i2i−2i−2i00000000002-200002i−2i000000
χ22222222-2-2-2-2-2-22-2200000002i2i−2i−2i0000000000-220000−2i2i000000
χ23222222-2-2-2-2-2-22-220000000−2i−2i2i2i00000000002-20000−2i2i000000
χ24222222-2-2-2-2-2-22-220000000−2i−2i2i2i0000000000-2200002i−2i000000
χ252222-2-22-2-22222-2-200000002-22-20000002-200000000002-20000
χ262222-2-22-2-22222-2-200000002-22-2000000-220000000000-220000
χ272222-2-22-2-22222-2-20000000-22-220000002-20000000000-220000
χ282222-2-22-2-22222-2-20000000-22-22000000-2200000000002-20000
χ292222-2-2-22222-2-2-222222-2-2-200000000000000002-22-200000000
χ302222-2-2-22222-2-2-222222-2-2-20000000000000000-22-2200000000
χ312222-2-2-22222-2-2-22-2-2-2-222200000000000000002-2-2200000000
χ322222-2-2-22222-2-2-22-2-2-2-22220000000000000000-222-200000000
χ332222-2-2-222-2-2-222-222-2-222-22i−2i−2i2i2i2i−2i−2i00000000000000000000
χ342222-2-2-222-2-2-222-222-2-222-2−2i2i2i−2i−2i−2i2i2i00000000000000000000
χ352222-2-2-222-2-2-222-2-2-222-2-222i−2i−2i2i−2i−2i2i2i00000000000000000000
χ362222-2-2-222-2-2-222-2-2-222-2-22−2i2i2i−2i2i2i−2i−2i00000000000000000000
χ37444444-4-4-444-4-44-400000000000000000000000000000000000
χ384444-4-44-4-4-4-44-44400000000000000000000000000000000000
χ3944-4-44-44-4400-4000004-44-400000000000000000000000000000
χ4044-4-44-44-4400-400000-44-4400000000000000000000000000000
χ4144-4-44-4-44-4004000000000000002i2−2i22i2−2i200000000000000000000
χ4244-4-44-4-44-400400000000000000−2i22i2−2i22i200000000000000000000
χ4344-4-4-4444-400-40000000000000022−22−222200000000000000000000
χ4444-4-4-4444-400-400000000000000−222222−2200000000000000000000
χ4544-4-4-44-4-44004000004-4-4400000000000000000000000000000
χ4644-4-4-44-4-4400400000-444-400000000000000000000000000000
χ478-88-8000000000004i2−4i2000000000000000000000000000000000
χ488-88-800000000000−4i24i2000000000000000000000000000000000
χ498-8-88000008-8000000000000000000000000000000000000000
χ508-8-8800000-88000000000000000000000000000000000000000

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