Finite Group DatabasebetaFinite Group Databasebeta| order | 2436 |
| isoclinism | isoclinic class of C3⋊(D29⋊C7) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(Dic29⋊C7) |
| unambiguous semidirect product | Dic87⋊C7 |
| derived, Hall | C3×C29 ⋊ C4×C7 |
| Hall | C3×C29⋊C7 ⋊ C4 |
| Hall | Dic87 ⋊ C7 |
| Hall | C29⋊C7 ⋊ Dic3 |
| Sylow | C29 ⋊ C7×Dic3 |
| Sylow | C3 ⋊ Dic29⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊(D29⋊C7) |
| commutator, hypocenter | C3×C29 | C4×C7 |
| Fitting, socle, cosocle | C2×C3×C29 | C2×C7 |
| prime radical | C2×C3×C29⋊C7 | C2 |
| LCS | G ▷ C3×C29 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 348 |
Polycyclic presentation:
2,7,3,29,2|a^2=e,c^a=c^2,d^a=d^28,d^b=d^2354 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2436, 4);