Finite Group Databasebeta

← Group #176721

Character table — Group #176721

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size111111114444444444888888888816161616161616161616161616161616161616163232
order12222222444444444422244444444444444488888888888824
χ111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-11-1-11-1-1-1-111111111-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-11-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111-1-11-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1
χ61111111111111111111-1-11-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111-1-11-1-1-1-1-1-1-111-1-1-1111111-1-1-1-1-1-1-1-111
χ81111111111111111111-1-11-1-1-1-1-1-1-111-1-1-111-1-1-1-111111111-1-1
χ9111111111-1-111-1-1111-111-1-1-111-1-1-11-111-11-111-1-111-1-111-1-11-1
χ10111111111-1-111-1-1111-111-1-1-111-1-1-11-111-11-1-1-111-1-111-1-111-11
χ11111111111-1-111-1-1111-111-1-1-1-1-111-1-111-11-1111-1-111-1-1-1-111-11
χ12111111111-1-111-1-1111-111-1-1-1-1-111-1-111-11-11-1-111-1-11111-1-11-1
χ13111111111-1-111-1-1111-1-1-1-11111-1-11-11-11-1-1111-1-1-1-11111-1-1-11
χ14111111111-1-111-1-1111-1-1-1-11111-1-11-11-11-1-11-1-11111-1-1-1-1111-1
χ15111111111-1-111-1-1111-1-1-1-111-1-11111-1-1-111-111-1-1-1-111-1-1111-1
χ16111111111-1-111-1-1111-1-1-1-111-1-11111-1-1-111-1-1-11111-1-111-1-1-11
χ1722222222222-2-2-2-22-2-2200-20022-2-20000-220000000000000000
χ1822222222222-2-2-2-22-2-2200-200-2-22200002-20000000000000000
χ19222222222-2-2-2-2222-2-2-20020022220000-2-20000000000000000
χ20222222222-2-2-2-2222-2-2-200200-2-2-2-20000220000000000000000
χ2122222222-2222-222-22-2-222-2220000-200-2000000000000000000
χ2222222222-2222-222-22-2-2-2-2-2-2-200002002000000000000000000
χ2322222222-222-22-2-2-2-22-200200000002-2000-2200000000000000
χ2422222222-222-22-2-2-2-22-20020000000-220002-200000000000000
χ2522222222-2-2-22-2-2-2-22-22222-2-20000200-2000000000000000000
χ2622222222-2-2-22-2-2-2-22-22-2-22220000-2002000000000000000000
χ2722222222-2-2-2-2222-2-22200-2000000022000-2-200000000000000
χ2822222222-2-2-2-2222-2-22200-20000000-2-20002200000000000000
χ2944-4-444-4-4000004-40000000000000000000002i−2i2i−2i0000000000
χ3044-4-444-4-4000004-4000000000000000000000−2i2i−2i2i0000000000
χ3144-4-444-4-400000-440000000000000000000002i−2i−2i2i0000000000
χ3244-4-444-4-400000-44000000000000000000000−2i2i2i−2i0000000000
χ3344-4-4-4-44404i−4i0000000000000000000000000000000002-22i−2i00
χ3444-4-4-4-44404i−4i000000000000000000000000000000000-22−2i2i00
χ3544-4-4-4-4440−4i4i0000000000000000000000000000000002-2−2i2i00
χ3644-4-4-4-4440−4i4i000000000000000000000000000000000-222i−2i00
χ374-44-44-44-4000040000-40000000000000000000000002i2−2i2000000
χ384-44-44-44-4000040000-4000000000000000000000000−2i22i2000000
χ394-44-44-44-40000-400004000000000000000000000022−2200000000
χ404-44-44-44-40000-4000040000000000000000000000−222200000000
χ414-44-4-44-4400040000-4000004i−4i00000000000000000000000000
χ424-44-4-44-4400040000-400000−4i4i00000000000000000000000000
χ434-44-4-44-44000-400004004-400000000000000000000000000000
χ444-44-4-44-44000-40000400-4400000000000000000000000000000
χ454-4-44-444-44000000-400000000004i−4i0000000000000000000000
χ464-4-44-444-44000000-40000000000−4i4i0000000000000000000000
χ474-4-44-444-4-40000004000000004-4000000000000000000000000
χ484-4-44-444-4-4000000400000000-44000000000000000000000000
χ498888-8-8-8-8000000000000000000000000000000000000000000
χ508-8-888-8-88000000000000000000000000000000000000000000

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