Finite Group DatabasebetaFinite Group Databasebeta| order | 15952 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#16860614 |
| unambiguous semidirect product | (C2×#16860614)⋊C2 |
| Fitting | C22×C997 ⋊ C4 |
| Sylow | C997 ⋊ C22⋊C4 |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3988 |
Polycyclic presentation:
2^4,997|a^2=d,b^a=bc,e^a=e^161,e^d=e^9961006 conjugacy classes — view the full character table.
| maximal subgroup of | #44542359, #44542360, C2×C22⋊#16860614, … |
| maximal normal subgroup of | #44542359, #44542360, C2×C22⋊#16860614, … |
| maximal quotient of | (C2×#16860614)⋊C4, C22⋊#22547569, #44542358, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15952, 45);