Finite Group Databasebeta

← Group #173625

Character table — Group #173625

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size1111111144444444444488888888888881616161616161616161616161616161616163232
order12222222224444444444444444444444444444488888888888844
χ111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-111-1-1-1-11-1-11-1-1-1-111111-1-1-1-1-1-1-1-111
χ41111111111111111111111-1-111-1-1-1-11-1-11-1-1-1-11-1-1-1-111111111-1-1
χ511111111111111111111-1-111-1-1-1-1-1-1111-11-11-1-111111111-1-1-1-1-1-1
χ611111111111111111111-1-111-1-1-1-1-1-1111-11-11-1-1-1-1-1-1-1-1-1-1111111
χ711111111111111111111-1-1-1-1-1-111111-1-1-1-11-11-11111-1-1-1-11111-1-1
χ811111111111111111111-1-1-1-1-1-111111-1-1-1-11-11-1-1-1-1-11111-1-1-1-111
χ911111111-1-1-1-11-1-1111111111-1-111-1-1-1-1-11-1-111-111-1-111-1-111-1-11-1
χ1011111111-1-1-1-11-1-1111111111-1-111-1-1-1-1-11-1-111-1-1-111-1-111-1-111-11
χ1111111111-1-1-1-11-1-11111111-1-1-1-1-1-111-111111-1-1-111-1-1-1-111-1-1111-1
χ1211111111-1-1-1-11-1-11111111-1-1-1-1-1-111-111111-1-1-1-1-11111-1-111-1-1-11
χ1311111111-1-1-1-11-1-111111-1-11111-1-111-1-1-1-1-111-1111-1-111-1-1-1-111-11
χ1411111111-1-1-1-11-1-111111-1-11111-1-111-1-1-1-1-111-11-1-111-1-11111-1-11-1
χ1511111111-1-1-1-11-1-111111-1-1-1-11111-1-1-111-11-1-11111-1-1-1-11111-1-1-11
χ1611111111-1-1-1-11-1-111111-1-1-1-11111-1-1-111-11-1-111-1-11111-1-1-1-1111-1
χ17222222222222-2-2-2-222-2-22200220000-200-20000-200000000000000
χ18222222222222-2-2-2-222-2-2-2-200-2-20000-20020000200000000000000
χ192222222222-2-2222-2-2-22-20022000000-2220-20-20000000000000000
χ202222222222-2-2222-2-2-22-200-2-2000000-2-2-202020000000000000000
χ212222222222-2-2-2-2-22-2-2-2200000022-2-22000020-2000000000000000
χ222222222222-2-2-2-2-22-2-2-22000000-2-22220000-202000000000000000
χ2322222222-2-2222-2-2-2-2-22-200220000002-2-2020-20000000000000000
χ2422222222-2-2222-2-2-2-2-22-200-2-20000002220-2020000000000000000
χ2522222222-2-222-2222-2-2-220000002222-20000-20-2000000000000000
χ2622222222-2-222-2222-2-2-22000000-2-2-2-2-20000202000000000000000
χ2722222222-2-2-2-2-222-222-2-22200-2-20000200-20000200000000000000
χ2822222222-2-2-2-2-222-222-2-2-2-20022000020020000-200000000000000
χ2922-2-22-22-22-200-22-200020002i−2i00000002i−2i0000002−22−2i2−i2i2−i2000000
χ3022-2-22-22-22-200-22-200020002i−2i00000002i−2i000000−22−22−i2i2−i2i2000000
χ3122-2-22-22-22-200-22-20002000−2i2i0000000−2i2i0000002−22−2−i2i2−i2i2000000
χ3222-2-22-22-22-200-22-20002000−2i2i0000000−2i2i000000−22−22i2−i2i2−i2000000
χ3322-2-22-22-2-2200-2-2200020002i−2i0000000−2i2i0000002−2−22i2−i2−i2i2000000
χ3422-2-22-22-2-2200-2-2200020002i−2i0000000−2i2i000000−222−2−i2i2i2−i2000000
χ3522-2-22-22-2-2200-2-220002000−2i2i00000002i−2i0000002−2−22−i2i2i2−i2000000
χ3622-2-22-22-2-2200-2-220002000−2i2i00000002i−2i000000−222−2i2−i2−i2i2000000
χ37444-4-44-4-4000000004-40000004-4000000000000000000000000000
χ38444-4-44-4-4000000004-4000000-44000000000000000000000000000
χ39444-4-44-4-400000000-44004-40000000000000000000000000000000
χ40444-4-44-4-400000000-4400-440000000000000000000000000000000
χ4144-4-44-44-44-4004-44000-40000000000000000000000000000000000
χ4244-4-44-44-4-440044-4000-40000000000000000000000000000000000
χ434-4-44-444-4004i−4i000000000000000000000000000000000002-22i−2i00
χ444-4-44-444-4004i−4i00000000000000000000000000000000000-22−2i2i00
χ454-4-44-444-400−4i4i000000000000000000000000000000000002-2−2i2i00
χ464-4-44-444-400−4i4i00000000000000000000000000000000000-222i−2i00
χ474-4-4-444-4400000004000-4000000004i−4i00000000000000000000000
χ484-4-4-444-4400000004000-400000000−4i4i00000000000000000000000
χ494-4-4-444-440000000-400040000004-40000000000000000000000000
χ504-4-4-444-440000000-40004000000-440000000000000000000000000
χ5188-88-8-8-88000000000000000000000000000000000000000000000
χ528-8888-8-8-8000000000000000000000000000000000000000000000
χ538-88-8-8-888000000000000000000000000000000000000000000000

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