Finite Group DatabasebetaFinite Group Databasebeta| order | 34839 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, socle, derived, Hall | C72×C79 ⋊ C32 |
| Sylow | C79 ⋊ ΓL(1,𝔽8)2 |
| Sylow | C72 ⋊ C3×C79⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C79 | C32 |
| LCS | G ▷ C72×C79 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1659 |
Polycyclic presentation:
3^2,7^2,79|c^a=c^2,e^a=e^55,c^b=c^2,d^b=d^4519 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34839, 29);