Finite Group DatabasebetaFinite Group Databasebeta| order | 12300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×(C5⋊D5)⋊D41 |
| unambiguous semidirect product | D205⋊(C3×D5) |
| Fitting, socle, Hall | C3×C52×C41 ⋊ C22 |
| derived, Hall | C52×C41 ⋊ C22×C3 |
| Hall | C3×C41 ⋊ D52 |
| Hall | C3×C52 ⋊ C2×D41 |
| Sylow | C41 ⋊ C3×D52 |
| Sylow | C52 ⋊ C2×C3×D41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | (C5⋊D5)⋊D41 |
| commutator, cosocle, hypocenter | C52×C41 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C41 | C22 |
| LCS | G ▷ C52×C41 | |
| UCS | C1 ◁ C3 | |
96 conjugacy classes of subgroups.
888 conjugacy classes — view the full character table.
| maximal subgroup of | C9×(C5⋊D5)⋊D41, C3×((C5⋊D5)⋊C3)⋊D41, C32×(C5⋊D5)⋊D41, … |
| maximal normal subgroup of | C9×(C5⋊D5)⋊D41, C32×(C5⋊D5)⋊D41 |
| maximal quotient of | C9×(C5⋊D5)⋊D41, C32×(C5⋊D5)⋊D41, C3×D205⋊D15, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12300, 146);