Finite Group DatabasebetaFinite Group Databasebeta| order | 3616 |
| isoclinism | isoclinic class of #90673 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C4×#90673 |
| unambiguous semidirect product | D113⋊C42 |
| Fitting | C2×C4×C113 ⋊ C4 |
| derived, Sylow | C113 ⋊ C2×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #90673 |
| commutator, hypocenter | C113 | C2×C42 |
| Frattini | C2 | C22×#90673 |
| Fitting | C2×C4×C113 | C4 |
| socle | C22×C113 | C2×C4 |
| prime radical | C22×D113 | C22 |
| cosocle | C2×D113 | C23 |
| LCS | G ▷ C113 | |
| UCS | C1 ◁ C2×C4 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 904 |
256 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3616, 222);