Finite Group DatabasebetaFinite Group Databasebeta| order | 18700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C25 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C11⋊C25)⋊#595 |
| unambiguous semidirect product | (C11⋊#595)⋊C25 |
| derived, Hall | C11×C17 ⋊ C4×C25 |
| Hall | C17×C11⋊C25 ⋊ C4 |
| Hall | C11⋊#595 ⋊ C25 |
| Hall | C11⋊C25 ⋊ #595 |
| Sylow | C17 ⋊ Dic11⋊C25 |
| Sylow | C11 ⋊ C25×#595 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | (C11⋊C5)⋊#595 |
| commutator, hypocenter | C11×C17 | C4×C25 |
| Fitting, socle | C5×C11×C17 | C4×C5 |
| prime radical, cosocle | C5×C11×D17 | C2×C5 |
| LCS | G ▷ C11×C17 | |
| UCS | C1 ◁ C5 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4675 |
Polycyclic presentation:
2,5,2,11,17,5|a^2=c,b^5=f,d^a=d^10,e^a=e^13,d^b=d^4,e^c=e^16250 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18700, 14);