Finite Group DatabasebetaFinite Group Databasebeta| order | 3616 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×#14268655 |
| derived, Sylow | C113 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #90673 |
| commutator, hypocenter | C113 | C22×C8 |
| Frattini | C2 | C22×#90673 |
| Fitting | C2×C4×C113 | C4 |
| socle | C22×C113 | C2×C4 |
| prime radical | C22×D113 | C4 |
| cosocle | Dic113 | C23 |
| LCS | G ▷ C113 | |
| UCS | C1 ◁ C2×C4 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1808 |
256 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3616, 229);