Finite Group DatabasebetaFinite Group Databasebeta| order | 34122 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C47 · Schur multiplier (H2) = C11 |
| direct product | C2×C47×C112⋊C3 |
| unambiguous semidirect product | (C2×C112)⋊(C3×C47) |
| unambiguous semidirect product | (C2×C112×C47)⋊C3 |
| Fitting, socle, Hall | C2×C112×C47 ⋊ C3 |
| derived, Sylow | C112 ⋊ C2×C3×C47 |
| Hall | C112×C47 ⋊ C2×C3 |
| Hall | C2×C112 ⋊ C3×C47 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C47 | C112⋊C3 |
| commutator, cosocle, hypocenter | C112 | C2×C3×C47 |
| Frattini | C1 | G |
| Fitting, socle | C2×C112×C47 | C3 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C2×C47 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3102 |
4042 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34122, 15);