Finite Group DatabasebetaFinite Group Databasebeta| order | 34356 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C7×C409 ⋊ C3×C4 |
| Hall | C7×Dic409 ⋊ C3 |
| Hall | #22575221 ⋊ C4 |
| Hall | Dic409 ⋊ ΓL(1,𝔽8) |
| Sylow | C409 ⋊ C4×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ Dic409⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #31769842 |
| commutator, hypocenter | C7×C409 | C3×C4 |
| Fitting, socle, cosocle | C2×C7×C409 | C2×C3 |
| prime radical | C2×#22575221 | C2 |
| LCS | G ▷ C7×C409 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11452 |
Polycyclic presentation:
2,3,7,409,2|a^2=e,d^a=d^408,c^b=c^2,d^b=d^53972 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34356, 16);