Finite Group DatabasebetaFinite Group Databasebeta| order | 3616 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | C2×#14268661 |
| Fitting, socle | C2×C113 ⋊ C16 |
| derived, Sylow | C113 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #14268661 |
| commutator, hypocenter | C113 | C2×C16 |
| Frattini | C1 | G |
| Fitting, socle | C2×C113 | C16 |
| prime radical | C2×D113 | C8 |
| cosocle | #11744762 | C22 |
| LCS | G ▷ C113 | |
| UCS | C1 ◁ C2 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 226 |
46 conjugacy classes — view the full character table.
| maximal subgroup of | C2×AGL(1,𝔽113) |
| maximal normal subgroup of | C2×AGL(1,𝔽113) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3616, 246);