Finite Group DatabasebetaFinite Group Databasebeta| order | 3616 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| direct product | C4×#11744762 |
| unambiguous semidirect product | #90673⋊C8 |
| Fitting | C4×C113 ⋊ C8 |
| derived, Sylow | C113 ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #11744762 |
| commutator, hypocenter | C113 | C4×C8 |
| Frattini | C2 | C2×#11744762 |
| Fitting | C4×C113 | C8 |
| socle | C2×C113 | C2×C8 |
| prime radical | C2×D113 | C2×C4 |
| cosocle | C2×#90673 | C22 |
| LCS | G ▷ C113 | |
| UCS | C1 ◁ C4 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 452 |
88 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3616, 237);