Finite Group DatabasebetaFinite Group Databasebeta| order | 3728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | C2×#14272347 |
| Fitting, socle | C2×C233 ⋊ C8 |
| derived, Sylow | C233 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #14272347 |
| commutator, hypocenter | C233 | C2×C8 |
| Frattini | C1 | G |
| Fitting, socle | C2×C233 | C8 |
| prime radical | C2×D233 | C4 |
| cosocle | #11745400 | C22 |
| LCS | G ▷ C233 | |
| UCS | C1 ◁ C2 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 466 |
74 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3728, 53);