Finite Group DatabasebetaFinite Group Databasebeta| order | 12300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C25 · Schur multiplier (H2) = C1 |
| direct product | C3×#4223⋊C25 |
| unambiguous semidirect product | #4223⋊(C3×C25) |
| unambiguous semidirect product | (C3×#4223)⋊C25 |
| derived, Sylow | C41 ⋊ C3×C4×C25 |
| Hall | C3×C41⋊C25 ⋊ C4 |
| Hall | C41⋊C25 ⋊ C3×C4 |
| Hall | C3×#4223 ⋊ C25 |
| Hall | #4223 ⋊ C3×C25 |
| Hall | C3×C41 ⋊ C4×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | #4223⋊C5 |
| commutator, hypocenter | C41 | C3×C4×C25 |
| Frattini | C5 | C3×#4223⋊C5 |
| Fitting, socle | C3×C5×C41 | C4×C5 |
| prime radical | C3×C5×D41 | C2×C5 |
| cosocle | C5×D41 | C2×C3×C5 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C3×C5 | |
36 conjugacy classes of subgroups.
330 conjugacy classes — view the full character table.
| maximal subgroup of | C9×#4223⋊C25, C32×#4223⋊C25, C3×C3⋊(#4223⋊C25) |
| maximal normal subgroup of | C9×#4223⋊C25, C32×#4223⋊C25 |
| maximal quotient of | C9×#4223⋊C25, C32×#4223⋊C25, C3×C3⋊(#4223⋊C25) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12300, 14);