Finite Group DatabasebetaFinite Group Databasebeta| order | 15952 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#16860614 |
| Fitting | C4×C997 ⋊ C4 |
| Sylow | C997 ⋊ C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#16860614 |
| commutator, socle | C2×C997 | C2×C4 |
| Fitting | C4×C997 | C4 |
| prime radical, cosocle | C2×D997 | C22 |
| hypercenter | C4 | #16860614 |
| hypocenter | C997 | C4⋊C4 |
| LCS | G ▷ C2×C997 ▷ C997 | |
| UCS | C1 ◁ C2 ◁ C4 | |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3988 |
Polycyclic presentation:
2^4,997|a^2=d,b^2=c,b^a=bc,e^a=e^161,e^d=e^9961006 conjugacy classes — view the full character table.
| maximal subgroup of | #44542363, #44542364, #44542369, … |
| maximal normal subgroup of | #44542363, #44542364, #44542369, … |
| maximal quotient of | (C2×#16860614)⋊C4, C4⋊#22547569, #44542368, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15952, 46);