Finite Group DatabasebetaFinite Group Databasebeta| order | 18525 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C52⋊#10625202 |
| Fitting, socle, derived, Hall | C52×C13×C19 ⋊ C3 |
| Hall | C52×C19 ⋊ C13⋊C3 |
| Hall | C52×C13 ⋊ C19⋊C3 |
| Hall | C13×C19 ⋊ C52⋊C3 |
| Sylow | C52 ⋊ #10625202 |
| Sylow | C19 ⋊ C13⋊(C52⋊C3) |
| Sylow | C13 ⋊ C19⋊(C52⋊C3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C13×C19 | C3 |
| LCS | G ▷ C52×C13×C19 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3705 |
Polycyclic presentation:
3,5^2,13,19|b^a=b^3c^2,c^a=bc,d^a=d^3,e^a=e^72061 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49150227, #49150229, #49150232, … |
| maximal normal subgroup of | #49150227, #49150229, #49150232, … |
| maximal quotient of | C2×C52⋊#10625202 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18525, 7);