Finite Group DatabasebetaFinite Group Databasebeta| order | 12300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C5 |
| direct product | C52⋊C3×Dic41 |
| unambiguous semidirect product | (C52×Dic41)⋊C3 |
| derived, Hall | C52×C41 ⋊ C3×C4 |
| Hall | C52×Dic41 ⋊ C3 |
| Hall | C41×C52⋊C3 ⋊ C4 |
| Sylow | C41 ⋊ C4×C52⋊C3 |
| Sylow | C52 ⋊ C3×Dic41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C52⋊C3×D41 |
| commutator, hypocenter | C52×C41 | C3×C4 |
| Fitting, socle, cosocle | C2×C52×C41 | C2×C3 |
| prime radical | C2×C41×C52⋊C3 | C2 |
| LCS | G ▷ C52×C41 | |
| UCS | C1 ◁ C2 | |
36 conjugacy classes of subgroups.
484 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C52⋊C3×Dic41, C52⋊C3×Dic123 |
| maximal normal subgroup of | C3×C52⋊C3×Dic41 |
| maximal quotient of | Dic41×C52⋊C9, C3×C52⋊C3×Dic41, C52⋊C3×Dic123 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12300, 61);