Finite Group DatabasebetaFinite Group Databasebeta| order | 15675 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C25 · Schur multiplier (H2) = C1 |
| derived, Hall | C11×C19 ⋊ C3×C25 |
| Hall | C19×C11⋊C25 ⋊ C3 |
| Hall | C11×C19⋊C3 ⋊ C25 |
| Sylow | C19 ⋊ C3×C11⋊C25 |
| Sylow | C11 ⋊ C25×C19⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | C11⋊C5×C19⋊C3 |
| commutator, hypocenter | C11×C19 | C3×C25 |
| Fitting, socle, cosocle | C5×C11×C19 | C3×C5 |
| prime radical | C5×C11×C19⋊C3 | C5 |
| LCS | G ▷ C11×C19 | |
| UCS | C1 ◁ C5 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5225 |
315 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C19⋊C3×C11⋊C25, D19⋊C3×C11⋊C25, C19⋊C3×D11⋊C25, … |
| maximal normal subgroup of | C2×C19⋊C3×C11⋊C25, D19⋊C3×C11⋊C25, C19⋊C3×D11⋊C25, … |
| maximal quotient of | C2×C19⋊C3×C11⋊C25 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15675, 4);