Finite Group DatabasebetaFinite Group Databasebeta| order | 15675 |
| isoclinism | isoclinic class of C11⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C19×C25 · Schur multiplier (H2) = C1 |
| direct product | C3×C19×C11⋊C25 |
| unambiguous semidirect product | C11⋊(C3×C19×C25) |
| unambiguous semidirect product | (C3×C11)⋊(C19×C25) |
| unambiguous semidirect product | (C3×C11×C19)⋊C25 |
| derived, Sylow | C11 ⋊ C3×C19×C25 |
| Hall | C3×C11×C19 ⋊ C25 |
| Hall | C11×C19 ⋊ C3×C25 |
| Hall | C3×C11 ⋊ C19×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5×C19 | C11⋊C5 |
| commutator, hypocenter | C11 | C3×C19×C25 |
| Frattini | C5 | C3×C19×C11⋊C5 |
| Fitting, socle, prime radical | C3×C5×C11×C19 | C5 |
| cosocle | C5×C11 | C3×C5×C19 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C3×C5×C19 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15675 |
1995 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C3×C19×C11⋊C25, C3×D19×C11⋊C25, C3×C19×D11⋊C25, … |
| maximal normal subgroup of | C2×C3×C19×C11⋊C25, C3×D19×C11⋊C25, C3×C19×D11⋊C25, … |
| maximal quotient of | C2×C3×C19×C11⋊C25 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15675, 2);