Finite Group DatabasebetaFinite Group Databasebeta| order | 15675 |
| isoclinism | isoclinic class of C19⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C52×C11 · Schur multiplier (H2) = C5 |
| direct product | C52×C11×C19⋊C3 |
| unambiguous semidirect product | C19⋊(C3×C52×C11) |
| unambiguous semidirect product | (C5×C19)⋊(C3×C5×C11) |
| Fitting, socle, Hall | C52×C11×C19 ⋊ C3 |
| derived, Sylow | C19 ⋊ C3×C52×C11 |
| Hall | C52×C19 ⋊ C3×C11 |
| Hall | C11×C19 ⋊ C3×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52×C11 | C19⋊C3 |
| commutator, cosocle, hypocenter | C19 | C3×C52×C11 |
| Frattini | C1 | G |
| Fitting, socle | C52×C11×C19 | C3 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C52×C11 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5225 |
2475 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C52×C11×D19⋊C3, C52×C11⋊(D19⋊C3), C52×D11×C19⋊C3, … |
| maximal normal subgroup of | C52×C11×D19⋊C3, C52×C11⋊(D19⋊C3), C52×D11×C19⋊C3, … |
| maximal quotient of | C2×C52×C11×C19⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15675, 10);