Finite Group DatabasebetaFinite Group Databasebeta| order | 12300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×D25×D41 |
| unambiguous semidirect product | (C41×D25)⋊(C2×C3) |
| unambiguous semidirect product | (C25×D41)⋊(C2×C3) |
| unambiguous semidirect product | D1025⋊(C2×C3) |
| Fitting, Hall | C3×C25×C41 ⋊ C22 |
| derived, Hall | C25×C41 ⋊ C22×C3 |
| Hall | C3×C41 ⋊ C2×D25 |
| Hall | C3×C25 ⋊ C2×D41 |
| Sylow | C41 ⋊ C2×C3×D25 |
| Sylow | C25 ⋊ C2×C3×D41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D25×D41 |
| commutator, cosocle, hypocenter | C25×C41 | C22×C3 |
| Frattini | C5 | C3×D5×D41 |
| Fitting | C3×C25×C41 | C22 |
| socle | C3×C5×C41 | C2×D5 |
| LCS | G ▷ C25×C41 | |
| UCS | C1 ◁ C3 | |
60 conjugacy classes of subgroups.
924 conjugacy classes — view the full character table.
| maximal subgroup of | C9×D25×D41, C32×D25×D41, C3×D41×D75, … |
| maximal normal subgroup of | C9×D25×D41, C32×D25×D41 |
| maximal quotient of | C9×D25×D41, C32×D25×D41, C3×D41×D75, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12300, 28);