Finite Group Databasebeta

← Group #178974

Character table — Group #178974

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47
size11111111444444448888888161616161616161616161616161616161616161616163232
order12222222444444442244444224444444488888888888844
χ111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1
χ411111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111-1-111-1-111-11-1-1-111-1-11111-1-1-1-11111-1-1
χ61111111111111111-1-111-1-111-11-1-1-111-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111-1-111-1-11-11-11-1-1-1-1111111-1-1-1-1-1-1-1-111
χ81111111111111111-1-111-1-11-11-11-1-1-1-111-1-1-1-111111111-1-1
χ911111111-1-111111111-1-1-1-1-1111-11-1-1-11-111-1-111-1-111-1-11-1
χ1011111111-1-111111111-1-1-1-1-1111-11-1-1-11-1-1-111-1-111-1-111-11
χ1111111111-1-111111111-1-1-1-1-1-1-1-111-111-1111-1-111-1-1-1-111-11
χ1211111111-1-111111111-1-1-1-1-1-1-1-111-111-11-1-111-1-11111-1-11-1
χ1311111111-1-1111111-1-1-1-111-11-111-11-1-1-1111-1-1-1-11111-1-1-11
χ1411111111-1-1111111-1-1-1-111-11-111-11-1-1-11-1-11111-1-1-1-1111-1
χ1511111111-1-1111111-1-1-1-111-1-11-1-1-11111-111-1-1-1-111-1-1111-1
χ1611111111-1-1111111-1-1-1-111-1-11-1-1-11111-1-1-11111-1-111-1-1-11
χ1722222222222-2-2-2-22222-2-2-2-20000-22000000000000000000
χ1822222222222-2-2-2-22-2-22-222-200002-2000000000000000000
χ192222222222-222-2-2-200-2-200220-20002-20000000000000000
χ202222222222-222-2-2-200-2-2002-202000-220000000000000000
χ212222222222-2-2-222-200-2200-2020-20000-2200000000000000
χ222222222222-2-2-222-200-2200-20-20200002-200000000000000
χ2322222222-2-22-2-2-2-2222-222220000-2-2000000000000000000
χ2422222222-2-22-2-2-2-22-2-2-22-2-22000022000000000000000000
χ2522222222-2-2-222-2-2-2002200-220-2000-220000000000000000
χ2622222222-2-2-222-2-2-2002200-2-2020002-20000000000000000
χ2722222222-2-2-2-2-222-2002-200202020000-2-200000000000000
χ2822222222-2-2-2-2-222-2002-20020-20-200002200000000000000
χ2944-4-444-4-40004-40000000000000000000000000000002i2−2i200
χ3044-4-444-4-40004-4000000000000000000000000000000−2i22i200
χ3144-4-444-4-4000-4400000000000000000000000000002i2−2i20000
χ3244-4-444-4-4000-440000000000000000000000000000−2i22i20000
χ334-44-44-44-4000004-40000000000000000000000002i2−2i2000000
χ344-44-44-44-4000004-4000000000000000000000000−2i22i2000000
χ354-44-44-44-400000-4400000000000000000000002i2−2i200000000
χ364-44-44-44-400000-440000000000000000000000−2i22i200000000
χ374-44-4-44-440040000-400004i−4i0000000000000000000000000
χ384-44-4-44-440040000-40000−4i4i0000000000000000000000000
χ394-44-4-44-4400-4000044-400000000000000000000000000000
χ404-44-4-44-4400-400004-4400000000000000000000000000000
χ414-4-44-444-44-4000000000000000000000002i−2i2i−2i0000000000
χ424-4-44-444-44-400000000000000000000000−2i2i−2i2i0000000000
χ434-4-44-444-4-44000000000000000000000002i−2i−2i2i0000000000
χ444-4-44-444-4-4400000000000000000000000−2i2i2i−2i0000000000
χ458888-8-8-8-8000000000000000000000000000000000000000
χ4688-8-8-8-888000000000000000000000000000000000000000
χ478-8-888-8-88000000000000000000000000000000000000000

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