Finite Group DatabasebetaFinite Group Databasebeta| order | 34916 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #31775446⋊C2 |
| unambiguous semidirect product | #31775454⋊C2 |
| unambiguous semidirect product | #31775462⋊C2 |
| Fitting, socle, derived, Hall | C29×C43 ⋊ C22×C7 |
| Hall | #22576611 ⋊ C22 |
| Hall | D29×D43 ⋊ C7 |
| Sylow | C43 ⋊ C2×D29⋊C7 |
| Sylow | C29 ⋊ C2×D43⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C29×C43 | C22×C7 |
| LCS | G ▷ C29×C43 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1247 |
Polycyclic presentation:
2^2,7,29,43|e^a=e^42,d^b=d^28,d^c=d^16,e^c=e^2180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34916, 61);