Finite Group DatabasebetaFinite Group Databasebeta| order | 12540 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×D33⋊D19 |
| unambiguous semidirect product | D57⋊(C5×D11) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D33⋊D19 |
| commutator, cosocle, hypocenter | C3×C11×C19 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C11×C19 | C22 |
| LCS | G ▷ C3×C11×C19 | |
| UCS | C1 ◁ C5 | |
80 conjugacy classes of subgroups.
915 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D99⋊D19, C5×D33⋊(D19⋊C3), C3×C5×D33⋊D19, … |
| maximal normal subgroup of | C5×D33⋊(D19⋊C3), C3×C5×D33⋊D19 |
| maximal quotient of | C5×D99⋊D19, C3×C5×D33⋊D19, C5×D57⋊D33, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12540, 94);