Finite Group DatabasebetaFinite Group Databasebeta| order | 18700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊#13133352 |
| Fitting, socle, derived, Hall | C52×C11×C17 ⋊ C4 |
| Hall | C52×C17 ⋊ Dic11 |
| Hall | C52×C11 ⋊ Dic17 |
| Hall | C11×C17 ⋊ #1042 |
| Sylow | C52 ⋊ Dic187 |
| Sylow | C17 ⋊ C11⋊#1042 |
| Sylow | C11 ⋊ #13133352 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C11×C17 | C4 |
| prime radical, cosocle | C5×D5×C11×C17 | C2 |
| LCS | G ▷ C52×C11×C17 | |
| UCS | C1 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3740 |
Polycyclic presentation:
2^2,5^2,11,17|a^2=b,c^a=c^2,d^a=d^4,e^a=e^10,f^a=f^16,c^b=c^41873 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18700, 135);