Finite Group DatabasebetaFinite Group Databasebeta| order | 12300 |
| isoclinism | isoclinic class of C3⋊#4223 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×C3⋊#4223 |
| unambiguous semidirect product | C3⋊(C25×#4223) |
| Fitting, Hall | C3×C25×C41 ⋊ C4 |
| derived, Hall | C3×C41 ⋊ C4×C25 |
| Hall | C25×C41 ⋊ Dic3 |
| Hall | C3×C25 ⋊ #4223 |
| Sylow | C41 ⋊ Dic3×C25 |
| Sylow | C3 ⋊ C25×#4223 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | C3⋊#4223 |
| commutator, hypocenter | C3×C41 | C4×C25 |
| Frattini | C5 | C5×C3⋊#4223 |
| Fitting | C3×C25×C41 | C4 |
| socle | C3×C5×C41 | C4×C5 |
| prime radical, cosocle | C3×C5×D41 | C2×C5 |
| LCS | G ▷ C3×C41 | |
| UCS | C1 ◁ C25 | |
36 conjugacy classes of subgroups.
900 conjugacy classes — view the full character table.
| maximal subgroup of | C25×C9⋊#4223, C3×C25×C3⋊#4223, C25×C3⋊(C3⋊#4223) |
| maximal normal subgroup of | C3×C25×C3⋊#4223 |
| maximal quotient of | C25×C9⋊#4223, C3×C25×C3⋊#4223, C25×C3⋊(C3⋊#4223) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12300, 29);