Finite Group DatabasebetaFinite Group Databasebeta| order | 18525 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C19 · Schur multiplier (H2) = C5 |
| direct product | C19×C13⋊(C52⋊C3) |
| unambiguous semidirect product | C13⋊(C19×C52⋊C3) |
| unambiguous semidirect product | C52⋊(C19×C13⋊C3) |
| Fitting, socle, Hall | C52×C13×C19 ⋊ C3 |
| derived, Hall | C52×C13 ⋊ C3×C19 |
| Hall | C52×C19 ⋊ C13⋊C3 |
| Hall | C13×C19 ⋊ C52⋊C3 |
| Sylow | C52 ⋊ C19×C13⋊C3 |
| Sylow | C13 ⋊ C19×C52⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | C13⋊(C52⋊C3) |
| commutator, cosocle, hypocenter | C52×C13 | C3×C19 |
| Frattini | C1 | G |
| Fitting, socle | C52×C13×C19 | C3 |
| LCS | G ▷ C52×C13 | |
| UCS | C1 ◁ C19 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3705 |
2109 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C19×D13⋊(C52⋊C3), #49150231, D19×C13⋊(C52⋊C3), … |
| maximal normal subgroup of | C19×D13⋊(C52⋊C3), #49150231, D19×C13⋊(C52⋊C3), … |
| maximal quotient of | C2×C19×C13⋊(C52⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18525, 9);