Finite Group DatabasebetaFinite Group Databasebeta| order | 24186 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×D417 |
| unambiguous semidirect product | C3⋊(C29×D139) |
| unambiguous semidirect product | C139⋊(D3×C29) |
| Fitting, socle, Hall | C3×C29×C139 ⋊ C2 |
| derived, Hall | C3×C139 ⋊ C2×C29 |
| Hall | C29×C139 ⋊ D3 |
| Sylow | C139 ⋊ D3×C29 |
| Hall | C3×C29 ⋊ D139 |
| Sylow | C3 ⋊ C29×D139 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | D417 |
| commutator, cosocle, hypocenter | C3×C139 | C2×C29 |
| Frattini | C1 | G |
| Fitting, socle | C3×C29×C139 | C2 |
| LCS | G ▷ C3×C139 | |
| UCS | C1 ◁ C29 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12093 |
6090 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24186, 7);