Finite Group DatabasebetaFinite Group Databasebeta| order | 15675 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C52 · Schur multiplier (H2) = C5 |
| Fitting, socle | C5×C11×C19 ⋊ C3×C5 |
| derived, Hall | C11×C19 ⋊ C3×C52 |
| Hall | C5×C19×C11⋊C5 ⋊ C3 |
| Hall | C11×C19⋊C3 ⋊ C52 |
| Sylow | C19 ⋊ C3×C5×C11⋊C5 |
| Sylow | C11 ⋊ C52×C19⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C11⋊C5×C19⋊C3 |
| commutator, cosocle, hypocenter | C11×C19 | C3×C52 |
| Frattini | C1 | G |
| Fitting, socle | C5×C11×C19 | C3×C5 |
| LCS | G ▷ C11×C19 | |
| UCS | C1 ◁ C5 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1045 |
315 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15675, 6);