Finite Group Databasebeta

← Group #173635

Character table — Group #173635

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size1111111144444444444488888888888881616161616161616161616161616161616163232
order12222222224444444444444444444444424444488888888888844
χ111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111
χ411111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1
χ5111111111111111111111-1-111-1-1-1-111-1-1-1-11-11-111111111-1-1-1-1-1-1
χ6111111111111111111111-1-111-1-1-1-111-1-1-1-11-11-1-1-1-1-1-1-1-1-1111111
χ7111111111111111111111-1-1-1-111-1-1-1-111-1-1-11-111111-1-1-1-11111-1-1
χ8111111111111111111111-1-1-1-111-1-1-1-111-1-1-11-11-1-1-1-11111-1-1-1-111
χ911111111-1-111-1-1-1-11111-1111111-1-1-1-1-1-11-11-1-1111-1-111-1-111-1-11-1
χ1011111111-1-111-1-1-1-11111-1111111-1-1-1-1-1-11-11-1-11-1-111-1-111-1-111-11
χ1111111111-1-111-1-1-1-11111-111-1-1-1-1-1-111111-1-111-111-1-1-1-111-1-1111-1
χ1211111111-1-111-1-1-1-11111-111-1-1-1-1-1-111111-1-111-1-1-11111-1-111-1-1-11
χ1311111111-1-111-1-1-1-11111-1-1-111-1-111-1-111-1111-1-111-1-111-1-1-1-111-11
χ1411111111-1-111-1-1-1-11111-1-1-111-1-111-1-111-1111-1-1-1-111-1-11111-1-11-1
χ1511111111-1-111-1-1-1-11111-1-1-1-1-1111111-1-1-11-1-11111-1-1-1-11111-1-1-11
χ1611111111-1-111-1-1-1-11111-1-1-1-1-1111111-1-1-11-1-111-1-11111-1-1-1-1111-1
χ1722222222222-2-2-2-2-2-2-22-220000220000-2-200020-200000000000000
χ1822222222222-2-2-2-2-2-2-22-220000-2-2000022000-20200000000000000
χ192222222222-2222-2-2-2-2-22-200220000220000-20-2000000000000000
χ202222222222-2222-2-2-2-2-22-200-2-20000-2-20000202000000000000000
χ212222222222-2-2-2-22222-2-2-2220000220000-2-2000000000000000000
χ222222222222-2-2-2-22222-2-2-2-2-20000-2-2000022000000000000000000
χ2322222222-2-22-22222-2-22-2-2000022000022000-20-200000000000000
χ2422222222-2-22-22222-2-22-2-20000-2-20000-2-200020200000000000000
χ2522222222-2-2-22-2-222-2-2-22200220000-2-20000-202000000000000000
χ2622222222-2-2-22-2-222-2-2-22200-2-2000022000020-2000000000000000
χ2722222222-2-2-2-222-2-222-2-22220000-2-20000-22000000000000000000
χ2822222222-2-2-2-222-2-222-2-22-2-200002200002-2000000000000000000
χ29222-2-22-2-22-20-22-20000020002i−2i00002i−2i00000000i2−i2i2−i22−22−2000000
χ30222-2-22-2-22-20-22-20000020002i−2i00002i−2i00000000−i2i2−i2i2−22−22000000
χ31222-2-22-2-22-20-22-2000002000−2i2i0000−2i2i00000000i2−i2i2−i2−22−22000000
χ32222-2-22-2-22-20-22-2000002000−2i2i0000−2i2i00000000−i2i2−i2i22−22−2000000
χ33222-2-22-2-2-220-2-220000020002i−2i0000−2i2i00000000i2−i2−i2i22−2−22000000
χ34222-2-22-2-2-220-2-220000020002i−2i0000−2i2i00000000−i2i2i2−i2−222−2000000
χ35222-2-22-2-2-220-2-22000002000−2i2i00002i−2i00000000i2−i2−i2i2−222−2000000
χ36222-2-22-2-2-220-2-22000002000−2i2i00002i−2i00000000−i2i2i2−i22−2−22000000
χ37444-4-44-4-44-404-4400000-4000000000000000000000000000000000
χ38444-4-44-4-4-44044-400000-4000000000000000000000000000000000
χ3944-44-4-4-44000000004-40000000004i−4i000000000000000000000000
χ4044-44-4-4-44000000004-4000000000−4i4i000000000000000000000000
χ4144-44-4-4-4400000000-440004i−4i000000000000000000000000000000
χ4244-44-4-4-4400000000-44000−4i4i000000000000000000000000000000
χ434-4444-4-4-40040000000-40000004-400000000000000000000000000
χ444-4444-4-4-40040000000-4000000-4400000000000000000000000000
χ454-4444-4-4-400-4000000040000000000004i−4i00000000000000000000
χ464-4444-4-4-400-400000004000000000000−4i4i00000000000000000000
χ474-4-44-444-40000004i−4i00000000000000000000000000000002i−2i2-200
χ484-4-44-444-40000004i−4i0000000000000000000000000000000−2i2i-2200
χ494-4-44-444-4000000−4i4i00000000000000000000000000000002i−2i-2200
χ504-4-44-444-4000000−4i4i0000000000000000000000000000000−2i2i2-200
χ5188-8-88-88-8000000000000000000000000000000000000000000000
χ528-88-8-8-888000000000000000000000000000000000000000000000
χ538-8-8-888-88000000000000000000000000000000000000000000000

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