Finite Group DatabasebetaFinite Group Databasebeta| order | 3616 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C22×#11744762 |
| Fitting, socle | C22×C113 ⋊ C8 |
| derived, Sylow | C113 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #11744762 |
| commutator, hypocenter | C113 | C22×C8 |
| Frattini | C1 | G |
| Fitting, socle | C22×C113 | C8 |
| prime radical | C22×D113 | C4 |
| cosocle | #90673 | C23 |
| LCS | G ▷ C113 | |
| UCS | C1 ◁ C22 | |
76 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, 244);