Finite Group DatabasebetaFinite Group Databasebeta| order | 3844 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C31 |
| direct product | C2×C31⋊D31 |
| unambiguous semidirect product | (C2×C31)⋊D31 |
| Fitting, socle | C2×C312 ⋊ C2 |
| derived, Sylow | C312 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C31⋊D31 |
| commutator, cosocle, hypocenter | C312 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C312 | C2 |
| LCS | G ▷ C312 | |
| UCS | C1 ◁ C2 | |
170 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1922 |
964 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3844, 11);