Finite Group Databasebeta

← Group #173685

Character table — Group #173685

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size1111111144444444444488888888888881616161616161616161616161616161616163232
order12222222224444444444224444444444444444488888888888824
χ111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-11-1-1-1-11-11-1-1-111111111-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-11-1-1-1-11-11-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-1-1-111-1-1111-1-1-11-11-1-11111-1-1-1-1-1-1-1-111
χ611111111111111111111-1-1-1-111-1-1111-1-1-11-11-1-1-1-1-1-111111111-1-1
χ711111111111111111111-1-1-1-1-1-1111-1-111-1-1-1-1111111-1-1-1-11111-1-1
χ811111111111111111111-1-1-1-1-1-1111-1-111-1-1-1-111-1-1-1-11111-1-1-1-111
χ911111111-1-11-1-1-1-11111111-1-11111-1-1-1-1-11-1-11-1111-1-111-1-111-1-11-1
χ1011111111-1-11-1-1-1-11111111-1-11111-1-1-1-1-11-1-11-11-1-111-1-111-1-111-11
χ1111111111-1-11-1-1-1-11111111-1-1-1-1-1-1-1111111-1-11-111-1-111-1-1-1-111-11
χ1211111111-1-11-1-1-1-11111111-1-1-1-1-1-1-1111111-1-11-1-1-111-1-11111-1-11-1
χ1311111111-1-11-1-1-1-111111-1-11111-1-1-1-1-111-1-1111-111-1-1-1-111-1-1111-1
χ1411111111-1-11-1-1-1-111111-1-11111-1-1-1-1-111-1-1111-1-1-11111-1-111-1-1-11
χ1511111111-1-11-1-1-1-111111-1-111-1-111-111-1-1-111-1-1111-1-1-1-11111-1-1-11
χ1611111111-1-11-1-1-1-111111-1-111-1-111-111-1-1-111-1-11-1-11111-1-1-1-1111-1
χ172222222222222-2-2-2-2-22-222220000-20000-20-200000000000000000
χ182222222222222-2-2-2-2-22-2-2-2-2-20000-2000020200000000000000000
χ192222222222-2-2-222-222-2-200002200-222000-20-20000000000000000
χ202222222222-2-2-222-222-2-20000-2-200-2-2-20002020000000000000000
χ212222222222-2-2-2-2-22-2-2-2200000022200-2-200002-200000000000000
χ222222222222-2-2-2-2-22-2-2-22000000-2-2200220000-2200000000000000
χ2322222222-2-22-2-222-2-2-22-222-2-2000020000-20200000000000000000
χ2422222222-2-22-2-222-2-2-22-2-2-22200002000020-200000000000000000
χ2522222222-2-2-222222-2-2-2200000022-200220000-2-200000000000000
χ2622222222-2-2-222222-2-2-22000000-2-2-200-2-200002200000000000000
χ2722222222-2-2-222-2-2-222-2-2000022002-2-200020-20000000000000000
χ2822222222-2-2-222-2-2-222-2-20000-2-200222000-2020000000000000000
χ292222-2-2-2-22-2-22-200000202-22-2000000000000000i2−i2i2−i2i2−i2i2−i2000000
χ302222-2-2-2-22-2-22-200000202-22-2000000000000000−i2i2−i2i2−i2i2−i2i2000000
χ312222-2-2-2-22-2-22-20000020-22-22000000000000000i2−i2i2−i2−i2i2−i2i2000000
χ322222-2-2-2-22-2-22-20000020-22-22000000000000000−i2i2−i2i2i2−i2i2−i2000000
χ332222-2-2-2-2-22-2-2200000202-2-22000000000000000i2−i2−i2i2i2−i2−i2i2000000
χ342222-2-2-2-2-22-2-2200000202-2-22000000000000000−i2i2i2−i2−i2i2i2−i2000000
χ352222-2-2-2-2-22-2-220000020-222-2000000000000000i2−i2−i2i2−i2i2i2−i2000000
χ362222-2-2-2-2-22-2-220000020-222-2000000000000000−i2i2i2−i2i2−i2−i2i2000000
χ374444-4-4-4-44-44-4400000-40000000000000000000000000000000000
χ384444-4-4-4-4-4444-400000-40000000000000000000000000000000000
χ3944-4-444-4-4000004i−4i000000000000000000000000000000002-22i−2i00
χ4044-4-444-4-4000004i−4i00000000000000000000000000000000-22−2i2i00
χ4144-4-444-4-400000−4i4i000000000000000000000000000000002-2−2i2i00
χ4244-4-444-4-400000−4i4i00000000000000000000000000000000-222i−2i00
χ434-44-44-44-4000000004-4000000000004i−4i0000000000000000000000
χ444-44-44-44-4000000004-400000000000−4i4i0000000000000000000000
χ454-44-44-44-400000000-440000004i−4i000000000000000000000000000
χ464-44-44-44-400000000-44000000−4i4i000000000000000000000000000
χ474-4-444-4-4400000004000-40000004i−4i0000000000000000000000000
χ484-4-444-4-4400000004000-4000000−4i4i0000000000000000000000000
χ494-4-444-4-440000000-40004000000000004-400000000000000000000
χ504-4-444-4-440000000-4000400000000000-4400000000000000000000
χ5188-8-8-8-888000000000000000000000000000000000000000000000
χ528-88-8-88-88000000000000000000000000000000000000000000000
χ538-8-88-888-8000000000000000000000000000000000000000000000

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