Finite Group DatabasebetaFinite Group Databasebeta| order | 3688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | C4×D461 |
| Fitting | C4×C461 ⋊ C2 |
| derived, Sylow | C461 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | D461 |
| commutator, hypocenter | C461 | C2×C4 |
| Frattini | C2 | C2×D461 |
| Fitting | C4×C461 | C2 |
| socle, cosocle | C2×C461 | C22 |
| prime radical | C2×D461 | C2 |
| LCS | G ▷ C461 | |
| UCS | C1 ◁ C4 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1844 |
928 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3688, 7);