Finite Group Databasebeta

← Group #176313

Character table — Group #176313

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size1111111122224444448888888888888881616161616161616161616161616161616163232
order12222222444444444444444444444444444444488888888888822
χ111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1
χ41111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1
χ6111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111
χ8111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1
χ911111111-1-1-1-1111111-1-1-111-1-111-1-111-1-11-11-11-111-1-111-1-111-1-11-1
χ1011111111-1-1-1-1111111-1-1-111-1-111-1-111-1-11-11-11-1-1-111-1-111-1-111-11
χ1111111111-1-1-1-1111111-1-1-111-1-1-1-111-1-1111-1-11-1111-1-111-1-1-1-111-11
χ1211111111-1-1-1-1111111-1-1-111-1-1-1-111-1-1111-1-11-11-1-111-1-11111-1-11-1
χ1311111111-1-1-1-1111111-1-1-1-1-11111-1-1-1-111-111-1-1111-1-1-1-11111-1-1-11
χ1411111111-1-1-1-1111111-1-1-1-1-11111-1-1-1-111-111-1-11-1-11111-1-1-1-1111-1
χ1511111111-1-1-1-1111111-1-1-1-1-111-1-11111-1-1-11-111-111-1-1-1-111-1-1111-1
χ1611111111-1-1-1-1111111-1-1-1-1-111-1-11111-1-1-11-111-1-1-11111-1-111-1-1-11
χ172222222222222-2-22-2-22-2-20000000022220000-2-200000000000000
χ182222222222222-2-22-2-22-2-200000000-2-2-2-200002200000000000000
χ19222222222222-22-2-22-2-22-200002222000000-2-20000000000000000
χ20222222222222-22-2-22-2-22-20000-2-2-2-2000000220000000000000000
χ21222222222222-2-22-2-22-2-22222200000000-2-2000000000000000000
χ22222222222222-2-22-2-22-2-22-2-2-2-20000000022000000000000000000
χ2322222222-2-2-2-22-2-22-2-2-2220000000022-2-20000-2200000000000000
χ2422222222-2-2-2-22-2-22-2-2-22200000000-2-22200002-200000000000000
χ2522222222-2-2-2-2-22-2-22-22-22000022-2-2000000-220000000000000000
χ2622222222-2-2-2-2-22-2-22-22-220000-2-2220000002-20000000000000000
χ2722222222-2-2-2-2-2-22-2-2222-222-2-200000000-22000000000000000000
χ2822222222-2-2-2-2-2-22-2-2222-2-2-222000000002-2000000000000000000
χ294444-4-4-4-444-4-40000000000000000000000000002i−2i2i−2i0000000000
χ304444-4-4-4-444-4-4000000000000000000000000000−2i2i−2i2i0000000000
χ314444-4-4-4-4-4-4440000000000000000000000000002i−2i−2i2i0000000000
χ324444-4-4-4-4-4-444000000000000000000000000000−2i2i2i−2i0000000000
χ3344-4-444-4-44-44-400000000000000000000000000000002i−2i2i−2i000000
χ3444-4-444-4-44-44-40000000000000000000000000000000−2i2i−2i2i000000
χ3544-4-444-4-4-44-4400000000000000000000000000000002i−2i−2i2i000000
χ3644-4-444-4-4-44-440000000000000000000000000000000−2i2i2i−2i000000
χ3744-4-4-4-4444-4-44000000000000000000000000000000000002i−2i2i−2i00
χ3844-4-4-4-4444-4-4400000000000000000000000000000000000−2i2i−2i2i00
χ3944-4-4-4-444-444-4000000000000000000000000000000000002i−2i−2i2i00
χ4044-4-4-4-444-444-400000000000000000000000000000000000−2i2i2i−2i00
χ414-44-44-44-4000000400-4000004i−4i0000000000000000000000000000
χ424-44-44-44-4000000400-400000−4i4i0000000000000000000000000000
χ434-44-44-44-4000000-40040004-4000000000000000000000000000000
χ444-44-44-44-4000000-4004000-44000000000000000000000000000000
χ454-44-4-44-4400000400-4000000004i−4i00000000000000000000000000
χ464-44-4-44-4400000400-400000000−4i4i00000000000000000000000000
χ474-44-4-44-4400000-400400000000004-4000000000000000000000000
χ484-44-4-44-4400000-40040000000000-44000000000000000000000000
χ494-4-444-4-440000400-40000000000000004i−4i00000000000000000000
χ504-4-444-4-440000400-4000000000000000−4i4i00000000000000000000
χ514-4-444-4-440000-400400000000000004-40000000000000000000000
χ524-4-444-4-440000-40040000000000000-440000000000000000000000
χ538-8-88-888-8000000000000000000000000000000000000000000000

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