Finite Group DatabasebetaFinite Group Databasebeta| order | 34100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C25 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #30684714⋊C2 |
| unambiguous semidirect product | #30684720⋊C2 |
| unambiguous semidirect product | #30684726⋊C2 |
| derived, Hall | C11×C31 ⋊ C22×C25 |
| Hall | #22555294 ⋊ C22 |
| Hall | D11×D31 ⋊ C25 |
| Sylow | C31 ⋊ C2×D11⋊C25 |
| Sylow | C11 ⋊ C2×D31⋊C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | #16811774⋊C2 |
| commutator, hypocenter | C11×C31 | C22×C25 |
| Fitting, socle, cosocle | C5×C11×C31 | C22×C5 |
| prime radical | C5×D11×D31 | C5 |
| LCS | G ▷ C11×C31 | |
| UCS | C1 ◁ C5 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8525 |
Polycyclic presentation:
2^2,5,11,31,5|c^5=f,e^a=e^30,d^b=d^10,d^c=d^4,e^c=e^2215 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34100, 35);