Finite Group DatabasebetaFinite Group Databasebeta| order | 12300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C25 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic41⋊C25 |
| unambiguous semidirect product | Dic41⋊(C3×C25) |
| unambiguous semidirect product | (C3×Dic41)⋊C25 |
| derived, Sylow | C41 ⋊ C3×C4×C25 |
| Hall | C3×C41⋊C25 ⋊ C4 |
| Hall | C41⋊C25 ⋊ C3×C4 |
| Hall | C3×Dic41 ⋊ C25 |
| Hall | Dic41 ⋊ C3×C25 |
| Hall | C3×C41 ⋊ C4×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C5 | D41⋊C5 |
| commutator, hypocenter | C41 | C3×C4×C25 |
| Frattini | C2×C5 | C3×D41⋊C5 |
| Fitting, socle, prime radical | C2×C3×C5×C41 | C2×C5 |
| cosocle | C2×C5×C41 | C2×C3×C5 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C2×C3×C5 | |
36 conjugacy classes of subgroups.
420 conjugacy classes — view the full character table.
| maximal subgroup of | C9×Dic41⋊C25, C32×Dic41⋊C25, C3×C3⋊(Dic41⋊C25) |
| maximal normal subgroup of | C9×Dic41⋊C25, C32×Dic41⋊C25 |
| maximal quotient of | C9×Dic41⋊C25, C32×Dic41⋊C25, C3×C3⋊(Dic41⋊C25) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12300, 2);