Finite Group DatabasebetaFinite Group Databasebeta| order | 18700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C52 · Schur multiplier (H2) = C5 |
| direct product | C5×(C11⋊C5)⋊#595 |
| unambiguous semidirect product | (C11⋊C5)⋊(C5×#595) |
| unambiguous semidirect product | (C11⋊#595)⋊C52 |
| unambiguous semidirect product | (C5×C11⋊#595)⋊C5 |
| Fitting, socle | C5×C11×C17 ⋊ C4×C5 |
| derived, Hall | C11×C17 ⋊ C4×C52 |
| Hall | C5×C17×C11⋊C5 ⋊ C4 |
| Hall | C11⋊#595 ⋊ C52 |
| Hall | C5×C11⋊C5 ⋊ #595 |
| Sylow | C17 ⋊ C5×Dic11⋊C5 |
| Sylow | C11 ⋊ C52×#595 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | (C11⋊C5)⋊#595 |
| commutator, hypocenter | C11×C17 | C4×C52 |
| Frattini | C1 | G |
| Fitting, socle | C5×C11×C17 | C4×C5 |
| prime radical | C5×D17×C11⋊C5 | C2 |
| cosocle | C11×D17 | C2×C52 |
| LCS | G ▷ C11×C17 | |
| UCS | C1 ◁ C5 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 935 |
250 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18700, 68);