Finite Group DatabasebetaFinite Group Databasebeta| order | 34307 |
| automorphism | ? |
| homology | Abelianization (H1) = C7 · Schur multiplier (H2) = C13 |
No aliases for this group.
| Fitting, socle, derived, Hall | C132×C29 ⋊ C7 |
| Sylow | C132 ⋊ C29⋊C7 |
| Sylow | C29 ⋊ C132⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C132×C29 | C7 |
| LCS | G ▷ C132×C29 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2639 |
Polycyclic presentation:
7,13^2,29|b^a=b^6c^2,c^a=b^9c,d^a=d^16707 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34307, 5);