Finite Group DatabasebetaFinite Group Databasebeta| order | 34100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C52 · Schur multiplier (H2) = C5 |
| derived, Hall | C11×C31 ⋊ C4×C52 |
| Hall | C11⋊C5×ΓL(1,𝔽32) ⋊ C4 |
| Hall | Dic341 ⋊ C52 |
| Sylow | C31 ⋊ C5×Dic11⋊C5 |
| Sylow | C11 ⋊ C5×Dic31⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | (C11⋊C5)⋊(D31⋊C5) |
| commutator, hypocenter | C11×C31 | C4×C52 |
| Fitting, socle, cosocle | C2×C11×C31 | C2×C52 |
| prime radical | C2×C11⋊C5×ΓL(1,𝔽32) | C2 |
| LCS | G ▷ C11×C31 | |
| UCS | C1 ◁ C2 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1364 |
Polycyclic presentation:
2,5^2,11,31,2|a^2=f,d^a=d^10,e^a=e^30,e^b=e^16,d^c=d^4152 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34100, 83);