Finite Group DatabasebetaFinite Group Databasebeta| order | 34100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊(C31⋊#1042) |
| unambiguous semidirect product | C31⋊(C11⋊#1042) |
| Fitting, socle, derived, Hall | C52×C11×C31 ⋊ C4 |
| Hall | C52×C31 ⋊ Dic11 |
| Hall | C11×C31 ⋊ #1042 |
| Hall | C52×C11 ⋊ Dic31 |
| Sylow | C31 ⋊ C11⋊#1042 |
| Sylow | C52 ⋊ Dic341 |
| Sylow | C11 ⋊ C31⋊#1042 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C11×C31 | C4 |
| prime radical, cosocle | C5×D5×C11×C31 | C2 |
| LCS | G ▷ C52×C11×C31 | |
| UCS | C1 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6820 |
Polycyclic presentation:
2^2,5^2,11,31|a^2=b,c^a=c^2,d^a=d^4,e^a=e^10,f^a=f^30,c^b=c^43413 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34100, 280);