Finite Group DatabasebetaFinite Group Databasebeta| order | 34916 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C29×C43 ⋊ C4×C7 |
| Hall | #22576609 ⋊ C4 |
| Hall | C43×Dic29 ⋊ C7 |
| Hall | Dic29 ⋊ C43⋊C7 |
| Sylow | C43 ⋊ Dic29⋊C7 |
| Sylow | C29 ⋊ C4×C43⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #31775453 |
| commutator, hypocenter | C29×C43 | C4×C7 |
| Fitting, socle, cosocle | C2×C29×C43 | C2×C7 |
| prime radical | C2×#22576609 | C2 |
| LCS | G ▷ C29×C43 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4988 |
Polycyclic presentation:
2,7,29,43,2|a^2=e,c^a=c^28,c^b=c^16,d^b=d^11224 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34916, 31);