Finite Group Databasebeta

← Group #175394

Character table — Group #175394

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11111111444444444444888888888161616161616161616161616161616161616161616161616
order12222222444444444444222444444444444444444888888888888
χ111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-11-1-1-1111-1-1-1111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111-1-1-1-11-1-1-1-1-11-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111-1-1-1-11111-11-1-111-11-1-111-1-1-1-11111-1-1-1-1
χ6111111111111111111111-1-1-1-11111-11-1-1-1-1-11-1-1-1-11111-1-1-1-11111
χ7111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111
χ8111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111111111-1-1-1-1
χ911111111-1-11-1-11-1-11111-111-1-111-1-11-11111-11-1-1-1-111-1-111-1-111-1-1
χ1011111111-1-11-1-11-1-11111-111-1-111-1-11-111-1-1-11-1-111-1-111-1-111-1-111
χ1111111111-1-11-1-11-1-11111-111-1-1-1-11111-1-111-1-111-1-111-1-1-1-111-1-111
χ1211111111-1-11-1-11-1-11111-111-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-111-1-1
χ1311111111-1-11-1-11-1-11111-1-1-11111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ1411111111-1-11-1-11-1-11111-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ1511111111-1-11-1-11-1-11111-1-1-111-1-111-1111111-1-1-1-1-1-1-111-1-11111-1-1
χ1611111111-1-11-1-11-1-11111-1-1-111-1-111-1111-1-11-1-1-11111-1-111-1-1-1-111
χ1722222222222-2-2-222-2-22-2-2000022220-200000-20000000000000000
χ1822222222222-2-2-222-2-22-2-20000-2-2-2-2020000020000000000000000
χ192222222222-2222-2-2-2-2-22-200000000002-200002-200000000000000
χ202222222222-2222-2-2-2-2-22-20000000000-220000-2200000000000000
χ212222222222-2-2-2-2-2-222-2-2222220000-200000-200000000000000000
χ222222222222-2-2-2-2-2-222-2-22-2-2-2-20000200000200000000000000000
χ2322222222-2-2222-2-2-2-2-22-22000022-2-20200000-20000000000000000
χ2422222222-2-2222-2-2-2-2-22-220000-2-2220-20000020000000000000000
χ2522222222-2-2-222-22222-2-2-222-2-20000-200000200000000000000000
χ2622222222-2-2-222-22222-2-2-2-2-2220000200000-200000000000000000
χ2722222222-2-2-2-2-2222-2-2-22200000000002-20000-2200000000000000
χ2822222222-2-2-2-2-2222-2-2-2220000000000-2200002-200000000000000
χ294444-4-4-4-4000000004-4000004-40000000000000000000000000000
χ304444-4-4-4-4000000004-400000-440000000000000000000000000000
χ314444-4-4-4-400000000-440004-4000000000000000000000000000000
χ324444-4-4-4-400000000-44000-44000000000000000000000000000000
χ3344-4-444-4-40040000000-40000004-400000000000000000000000000
χ3444-4-444-4-40040000000-4000000-4400000000000000000000000000
χ3544-4-444-4-400-400000004000000004i−4i000000000000000000000000
χ3644-4-444-4-400-40000000400000000−4i4i000000000000000000000000
χ3744-4-4-4-4444i−4i0000000000000000000000000000000000000002-22i−2i
χ3844-4-4-4-4444i−4i000000000000000000000000000000000000000-22−2i2i
χ3944-4-4-4-444−4i4i0000000000000000000000000000000000000002-2−2i2i
χ4044-4-4-4-444−4i4i000000000000000000000000000000000000000-222i−2i
χ414-44-44-44-40000004-4000000000000000002i−2i00002i−2i000000000000
χ424-44-44-44-40000004-400000000000000000−2i2i0000−2i2i000000000000
χ434-44-44-44-4000000-44000000000000000002i−2i0000−2i2i000000000000
χ444-44-44-44-4000000-4400000000000000000−2i2i00002i−2i000000000000
χ454-44-4-44-440004i−4i00000000000000000000000000002i−2i2-200000000
χ464-44-4-44-440004i−4i0000000000000000000000000000−2i2i-2200000000
χ474-44-4-44-44000−4i4i00000000000000000000000000002i−2i-2200000000
χ484-44-4-44-44000−4i4i0000000000000000000000000000−2i2i2-200000000
χ494-4-44-444-400000400000-400000000000000000000000002i2−2i2000000
χ504-4-44-444-400000400000-40000000000000000000000000−2i22i2000000
χ514-4-44-444-400000-400000400000000000000000000000000022−220000
χ524-4-44-444-400000-4000004000000000000000000000000000−22220000
χ538-8-888-8-88000000000000000000000000000000000000000000000

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