Finite Group Databasebeta

← Group #175515

Character table — Group #175515

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11111111444444444444888888888161616161616161616161616161616161616161616161616
order12222222444444444444444444444224444444444888888888888
χ111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111-1-111-1-11-1-1-1-11-111-1111111-1-1-1-1-1-1-1-1
χ411111111111111111111111-1-111-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111-1-111-1-111-1-1-1-11-1-111111-1-1-1-1-1-1-1-11111
χ6111111111111111111111-1-111-1-111-1-1-1-11-1-1-1-11-1-111111111-1-1-1-1
χ7111111111111111111111-1-1-1-1-1-1-1-1-1111-1-1111-111-1-1-1-11111-1-1-1-1
χ8111111111111111111111-1-1-1-1-1-1-1-1-1111-1-11-1-1-1-1-11111-1-1-1-11111
χ911111111-1-1-1-11-1-111111-11111-1-1-1-1111-1-1-1-1111-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-11-1-111111-11111-1-1-1-1111-1-1-1-1-1-1111-1-111-1-111-1-111
χ1111111111-1-1-1-11-1-111111-111-1-1-1-1111-1-111-1111-1-1-111-1-1-1-111-1-111
χ1211111111-1-1-1-11-1-111111-111-1-1-1-1111-1-111-11-1-1-111-1-11111-1-111-1-1
χ1311111111-1-1-1-11-1-111111-1-1-11111-1-1-1-1-11-111111-1-1-1-111-1-11111-1-1
χ1411111111-1-1-1-11-1-111111-1-1-11111-1-1-1-1-11-111-1-111111-1-111-1-1-1-111
χ1511111111-1-1-1-11-1-111111-1-1-1-1-11111-111-111-111-1-1-1-1-11111-1-1-1-111
χ1611111111-1-1-1-11-1-111111-1-1-1-1-11111-111-111-1-1-1-11111-1-1-1-11111-1-1
χ17222222222222-2-2-222-2-2-2-20000000002-2-200200000000000000000
χ18222222222222-2-2-222-2-2-2-2000000000-22200-200000000000000000
χ192222222222-2-2222-2-2-2-22-2002200220000-20000-200000000000000
χ202222222222-2-2222-2-2-2-22-200-2-200-2-2000020000200000000000000
χ212222222222-2-2-2-2-2-2-222-2222002200-20000-2000000000000000000
χ222222222222-2-2-2-2-2-2-222-22-2-200-2-200200002000000000000000000
χ2322222222-2-2222-2-2-2-2-2-222002200-2-2000020000-200000000000000
χ2422222222-2-2222-2-2-2-2-2-22200-2-200220000-20000200000000000000
χ2522222222-2-222-222-2-222-2-22200-2-200-200002000000000000000000
χ2622222222-2-222-222-2-222-2-2-2-200220020000-2000000000000000000
χ2722222222-2-2-2-2-22222-2-2-220000000002-2200-200000000000000000
χ2822222222-2-2-2-2-22222-2-2-22000000000-22-200200000000000000000
χ294444-4-4-4-400000004-40000000000000000000000000000000022−2200
χ304444-4-4-4-400000004-400000000000000000000000000000000−222200
χ314444-4-4-4-40000000-44000000000000000000000000000000000022−22
χ324444-4-4-4-40000000-440000000000000000000000000000000000−2222
χ3344-4-44-4-444i−4i000000000000000000000000000000000002i−2i2-20000
χ3444-4-44-4-444i−4i00000000000000000000000000000000000−2i2i-220000
χ3544-4-44-4-44−4i4i000000000000000000000000000000000002i−2i-220000
χ3644-4-44-4-44−4i4i00000000000000000000000000000000000−2i2i2-20000
χ3744-4-4-444-4000004i−4i0000000000000000000002-202i−2i000000000000
χ3844-4-4-444-4000004i−4i000000000000000000000-220−2i2i000000000000
χ3944-4-4-444-400000−4i4i0000000000000000000002-20−2i2i000000000000
χ4044-4-4-444-400000−4i4i000000000000000000000-2202i−2i000000000000
χ414-44-444-4-400004000000-40004-40000000000000000000000000000
χ424-44-444-4-400004000000-4000-440000000000000000000000000000
χ434-44-444-4-40000-4000000400000004i−4i000000000000000000000000
χ444-44-444-4-40000-400000040000000−4i4i000000000000000000000000
χ454-44-4-4-444004-4000000000000000000000000000002-22-200000000
χ464-44-4-4-444004-400000000000000000000000000000-22-2200000000
χ474-44-4-4-44400-44000000000000000000000000000002-2-2200000000
χ484-44-4-4-44400-4400000000000000000000000000000-222-200000000
χ494-4-444-44-40000000004-40000004i−4i00000000000000000000000000
χ504-4-444-44-40000000004-4000000−4i4i00000000000000000000000000
χ514-4-444-44-4000000000-44004i−4i000000000000000000000000000000
χ524-4-444-44-4000000000-4400−4i4i000000000000000000000000000000
χ538-8-88-88-88000000000000000000000000000000000000000000000

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