Finite Group DatabasebetaFinite Group Databasebeta| order | 18700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×C11⋊#595 |
| Fitting, Hall | C11×C17×C25 ⋊ C4 |
| derived, Hall | C11×C17 ⋊ C4×C25 |
| Hall | C17×C25 ⋊ Dic11 |
| Hall | C11×C25 ⋊ #595 |
| Sylow | C17 ⋊ C25×Dic11 |
| Sylow | C11 ⋊ C25×#595 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | C11⋊#595 |
| commutator, hypocenter | C11×C17 | C4×C25 |
| Frattini | C5 | C5×C11⋊#595 |
| Fitting | C11×C17×C25 | C4 |
| socle | C5×C11×C17 | C4×C5 |
| prime radical, cosocle | C5×C11×D17 | C2×C5 |
| LCS | G ▷ C11×C17 | |
| UCS | C1 ◁ C25 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4675 |
1450 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18700, 22);