Finite Group DatabasebetaFinite Group Databasebeta| order | 2436 |
| isoclinism | isoclinic class of D7×D29 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×D7×D29 |
| Fitting, socle, Hall | C3×C7×C29 ⋊ C22 |
| derived, Hall | C7×C29 ⋊ C22×C3 |
| Hall | C3×C29 ⋊ C2×D7 |
| Sylow | C29 ⋊ C2×C3×D7 |
| Hall | C3×C7 ⋊ C2×D29 |
| Sylow | C7 ⋊ C2×C3×D29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D7×D29 |
| commutator, cosocle, hypocenter | C7×C29 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C29 | C22 |
| LCS | G ▷ C7×C29 | |
| UCS | C1 ◁ C3 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 609 |
240 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2436, 34);