Finite Group DatabasebetaFinite Group Databasebeta| order | 12300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C25 · Schur multiplier (H2) = C1 |
| direct product | Dic3×C41⋊C25 |
| unambiguous semidirect product | C3⋊(C4×C41⋊C25) |
| unambiguous semidirect product | (Dic3×C41)⋊C25 |
| derived, Hall | C3×C41 ⋊ C4×C25 |
| Hall | C3×C41⋊C25 ⋊ C4 |
| Hall | Dic3×C41 ⋊ C25 |
| Sylow | C41 ⋊ Dic3×C25 |
| Sylow | C3 ⋊ C4×C41⋊C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C5 | D3×C41⋊C5 |
| commutator, hypocenter | C3×C41 | C4×C25 |
| Fitting, socle, prime radical, cosocle | C2×C3×C5×C41 | C2×C5 |
| LCS | G ▷ C3×C41 | |
| UCS | C1 ◁ C2×C5 | |
36 conjugacy classes of subgroups.
390 conjugacy classes — view the full character table.
| maximal subgroup of | Dic9×C41⋊C25, C3×Dic3×C41⋊C25, C3⋊Dic3×C41⋊C25 |
| maximal normal subgroup of | C3×Dic3×C41⋊C25 |
| maximal quotient of | Dic9×C41⋊C25, C3×Dic3×C41⋊C25, C3⋊Dic3×C41⋊C25 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12300, 3);