Finite Group Databasebeta

← Group #173785

Character table — Group #173785

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size1111111144444444444488888888888881616161616161616161616161616161616163232
order12222222444444444444244444444444444444488888888888824
χ111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111-1-111-1-1-1-1-1-11-11-1-1-11111-1-1-1-1-1-1-1-111
χ411111111111111111111111-1-111-1-1-1-1-1-11-11-1-1-1-1-1-1-111111111-1-1
χ5111111111111111111111-1-111-1-111-1-1-1-1-1-1-11-1111111111-1-1-1-1-1-1
χ6111111111111111111111-1-111-1-111-1-1-1-1-1-1-11-11-1-1-1-1-1-1-1-1111111
χ7111111111111111111111-1-1-1-1-1-1-1-11111-11-1-11-11111-1-1-1-11111-1-1
χ8111111111111111111111-1-1-1-1-1-1-1-11111-11-1-11-1-1-1-1-11111-1-1-1-111
χ91111111111-1-1-1-1-1-11111-11111-1-1-1-111-1-1-1111-1-111-1-111-1-111-1-11-1
χ101111111111-1-1-1-1-1-11111-11111-1-1-1-111-1-1-1111-1-1-1-111-1-111-1-111-11
χ111111111111-1-1-1-1-1-11111-111-1-1-1-111-1-111-1-11-11111-1-1-1-111-1-1111-1
χ121111111111-1-1-1-1-1-11111-111-1-1-1-111-1-111-1-11-111-1-11111-1-111-1-1-11
χ131111111111-1-1-1-1-1-11111-1-1-11111-1-1-1-1111-1-111-111-1-111-1-1-1-111-11
χ141111111111-1-1-1-1-1-11111-1-1-11111-1-1-1-1111-1-111-1-1-111-1-11111-1-11-1
χ151111111111-1-1-1-1-1-11111-1-1-1-1-1111111-1-111-1-1-1111-1-1-1-11111-1-1-11
χ161111111111-1-1-1-1-1-11111-1-1-1-1-1111111-1-111-1-1-11-1-11111-1-1-1-1111-1
χ17222222222-22222-2-2-2-22-2-20000000022220-200-2000000000000000
χ18222222222-22222-2-2-2-22-2-200000000-2-2-2-202002000000000000000
χ19222222222-2-2-2-2-222-2-22-220000000022-2-20-2002000000000000000
χ20222222222-2-2-2-2-222-2-22-2200000000-2-2220200-2000000000000000
χ2122222222-2222-2-222-2-2-22-2002200220000000-20-200000000000000
χ2222222222-2222-2-222-2-2-22-200-2-200-2-2000000020200000000000000
χ2322222222-22-2-222-2-2-2-2-222002200-2-20000000-20200000000000000
χ2422222222-22-2-222-2-2-2-2-22200-2-20022000000020-200000000000000
χ2522222222-2-222-2-2-2-222-2-222200-2-200000020-200000000000000000
χ2622222222-2-222-2-2-2-222-2-22-2-20022000000-20200000000000000000
χ2722222222-2-2-2-2222222-2-2-2220022000000-20-200000000000000000
χ2822222222-2-2-2-2222222-2-2-2-2-200-2-200000020200000000000000000
χ292-2222-2-2-200002i−2i2i−2i2-20002-2002i−2i00000000000000002−2i2−i22−2i2−i200
χ302-2222-2-2-200002i−2i2i−2i2-20002-2002i−2i0000000000000000−22−i2i2−22−i2i200
χ312-2222-2-2-200002i−2i2i−2i2-2000-2200−2i2i00000000000000002−2i2−i2−22−i2i200
χ322-2222-2-2-200002i−2i2i−2i2-2000-2200−2i2i0000000000000000−22−i2i22−2i2−i200
χ332-2222-2-2-20000−2i2i−2i2i2-20002-200−2i2i00000000000000002−2−i2i22−2−i2i200
χ342-2222-2-2-20000−2i2i−2i2i2-20002-200−2i2i0000000000000000−22i2−i2−22i2−i200
χ352-2222-2-2-20000−2i2i−2i2i2-2000-22002i−2i00000000000000002−2−i2i2−22i2−i200
χ362-2222-2-2-20000−2i2i−2i2i2-2000-22002i−2i0000000000000000−22i2−i22−2−i2i200
χ3744-4-44-4-44004-40000000000000000000000000002i−2i2i−2i0000000000
χ3844-4-44-4-44004-4000000000000000000000000000−2i2i−2i2i0000000000
χ3944-4-44-4-4400-440000000000000000000000000002i−2i−2i2i0000000000
χ4044-4-44-4-4400-44000000000000000000000000000−2i2i2i−2i0000000000
χ414-4444-4-4-400004i−4i−4i4i-4400000000000000000000000000000000000
χ424-4444-4-4-40000−4i4i4i−4i-4400000000000000000000000000000000000
χ434-44-4-44-4404000000000-400000004i−4i000000000000000000000000
χ444-44-4-44-4404000000000-40000000−4i4i000000000000000000000000
χ454-44-4-44-440-400000000040004-40000000000000000000000000000
χ464-44-4-44-440-40000000004000-440000000000000000000000000000
χ474-4-44-4-4444000000000-400000000004i−4i0000000000000000000000
χ484-4-44-4-4444000000000-40000000000−4i4i0000000000000000000000
χ494-4-44-4-444-400000000040000000000004-400000000000000000000
χ504-4-44-4-444-40000000004000000000000-4400000000000000000000
χ51888-8-8-88-8000000000000000000000000000000000000000000000
χ5288-88-88-8-8000000000000000000000000000000000000000000000
χ538-8-8-8888-8000000000000000000000000000000000000000000000

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