Finite Group DatabasebetaFinite Group Databasebeta| order | 12540 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C19⋊C3×Dic55 |
| unambiguous semidirect product | C11⋊(Dic5×C19⋊C3) |
| unambiguous semidirect product | (C19×Dic55)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C19⋊C3×D55 |
| commutator, hypocenter | C5×C11×C19 | C3×C4 |
| Fitting, socle, cosocle | C2×C5×C11×C19 | C2×C3 |
| prime radical | C2×C5×C11×C19⋊C3 | C2 |
| LCS | G ▷ C5×C11×C19 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
522 conjugacy classes — view the full character table.
| maximal subgroup of | #4296×Dic55, C3×C19⋊C3×Dic55, C19⋊C3×Dic165 |
| maximal normal subgroup of | #4296×Dic55, C3×C19⋊C3×Dic55 |
| maximal quotient of | #4294×Dic55, C3×C19⋊C3×Dic55, C19⋊C3×Dic165 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12540, 32);