Finite Group DatabasebetaFinite Group Databasebeta| order | 15675 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C11 · Schur multiplier (H2) = C5 |
| Fitting, socle, Hall | C52×C11×C19 ⋊ C3 |
| derived, Hall | C52×C19 ⋊ C3×C11 |
| Hall | C52×C11 ⋊ C19⋊C3 |
| Hall | C11×C19 ⋊ C52⋊C3 |
| Sylow | C52 ⋊ C11×C19⋊C3 |
| Sylow | C19 ⋊ C11×C52⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C19⋊(C52⋊C3) |
| commutator, cosocle, hypocenter | C52×C19 | C3×C11 |
| Frattini | C1 | G |
| Fitting, socle | C52×C11×C19 | C3 |
| LCS | G ▷ C52×C19 | |
| UCS | C1 ◁ C11 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3135 |
1771 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×D19⋊(C52⋊C3), C11⋊(D19⋊(C52⋊C3)), D11×C19⋊(C52⋊C3), … |
| maximal normal subgroup of | C11×D19⋊(C52⋊C3), C11⋊(D19⋊(C52⋊C3)), D11×C19⋊(C52⋊C3), … |
| maximal quotient of | C2×C11×C19⋊(C52⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15675, 8);