Finite Group Databasebeta

← Group #98342

Character table — Group #98342

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11111111444444444444888888888161616161616161616161616161616161616161616161616
order12222222444444444444444444444444444448888888888888888
χ111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-11-1-1-11-1-1-11111-1-1-1-11111-1-1-1-1
χ41111111111111111111111111-1-1-1-11-1-1-11-1-1-1-1-1-1-11111-1-1-1-11111
χ5111111111111111111111-1-1-1-11111-11-1-1-11-1-111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111-1-1-1-11111-11-1-1-11-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1111ii−i−iii−i−iii−i−iii−i−i
χ10111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1111−i−iii−i−iii−i−iii−i−iii
χ11111111111111-1-1-1-1-1-1-1-111111-1-111-1111-1-1-1-1ii−i−i−i−iiiii−i−i−i−iii
χ12111111111111-1-1-1-1-1-1-1-111111-1-111-1111-1-1-1-1−i−iiiii−i−i−i−iiiii−i−i
χ13111111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-11-11111-1-1ii−i−iii−i−i−i−iii−i−iii
χ14111111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-11-11111-1-1−i−iii−i−iiiii−i−iii−i−i
χ15111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-11111-1-11-111ii−i−i−i−iii−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-11111-1-11-111−i−iiiii−i−iii−i−i−i−iii
χ172222222222-2-222-2-2-2-222-2000022-2-202000-2000000000000000000
χ182222222222-2-222-2-2-2-222-20000-2-2220-20002000000000000000000
χ192222222222-2-2-2-22222-2-2-2000022220-2000-2000000000000000000
χ202222222222-2-2-2-22222-2-2-20000-2-2-2-2020002000000000000000000
χ2122222222-2-2222-222-2-22-2-222-2-200002000-20000000000000000000
χ2222222222-2-2222-222-2-22-2-2-2-2220000-200020000000000000000000
χ2322222222-2-222-22-2-222-22-222-2-20000-200020000000000000000000
χ2422222222-2-222-22-2-222-22-2-2-22200002000-20000000000000000000
χ2522222222-2-2-2-22-2-2-2222-2200000000002-2002-20000000000000000
χ2622222222-2-2-2-22-2-2-2222-220000000000-2200-220000000000000000
χ2722222222-2-2-2-2-2222-2-2-22200000000002-200-220000000000000000
χ2822222222-2-2-2-2-2222-2-2-2220000000000-22002-20000000000000000
χ29222-2-2-2-222-200002i−2i2i−2i00000002i−2i2-200000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i
χ30222-2-2-2-222-200002i−2i2i−2i00000002i−2i2-20000000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i
χ31222-2-2-2-222-200002i−2i2i−2i0000000−2i2i-2200000000000000001−i−1+i1+i−1−i−1−i1+i−1+i1−i
χ32222-2-2-2-222-200002i−2i2i−2i0000000−2i2i-220000000000000000−1+i1−i−1−i1+i1+i−1−i1−i−1+i
χ33222-2-2-2-222-20000−2i2i−2i2i00000002i−2i-2200000000000000001+i−1−i1−i−1+i−1+i1−i−1−i1+i
χ34222-2-2-2-222-20000−2i2i−2i2i00000002i−2i-220000000000000000−1−i1+i−1+i1−i1−i−1+i1+i−1−i
χ35222-2-2-2-222-20000−2i2i−2i2i0000000−2i2i2-200000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i
χ36222-2-2-2-222-20000−2i2i−2i2i0000000−2i2i2-20000000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i
χ37444-4-4-4-44-4400004i−4i−4i4i00000000000000000000000000000000000
χ38444-4-4-4-44-440000−4i4i4i−4i00000000000000000000000000000000000
χ3944-444-4-4-4004-4000000000004-40000000000000000000000000000
χ4044-444-4-4-4004-400000000000-440000000000000000000000000000
χ4144-444-4-4-400-440000000004-4000000000000000000000000000000
χ4244-444-4-4-400-44000000000-44000000000000000000000000000000
χ434-444-44-4-40000400000-400000000000000000000002-22-200000000
χ444-444-44-4-40000400000-40000000000000000000000-22-2200000000
χ454-444-44-4-40000-400000400000000000000000000002i−2i−2i2i00000000
χ464-444-44-4-40000-40000040000000000000000000000−2i2i2i−2i00000000
χ474-4-44-4-44400000400000-4000000000000000002i−2i2i−2i000000000000
χ484-4-44-4-44400000400000-400000000000000000−2i2i−2i2i000000000000
χ494-4-44-4-44400000-4000004000000000000000002-2-22000000000000
χ504-4-44-4-44400000-400000400000000000000000-222-2000000000000
χ5188-8-8-888-8000000000000000000000000000000000000000000000
χ528-88-88-88-8000000000000000000000000000000000000000000000
χ538-8-8-888-88000000000000000000000000000000000000000000000

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