Finite Group DatabasebetaFinite Group Databasebeta| order | 12300 |
| isoclinism | isoclinic class of C3⋊#4223 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C52 · Schur multiplier (H2) = C5 |
| direct product | C52×C3⋊#4223 |
| unambiguous semidirect product | C3⋊(C52×#4223) |
| Fitting, socle, Hall | C3×C52×C41 ⋊ C4 |
| derived, Hall | C3×C41 ⋊ C4×C52 |
| Hall | C52×C41 ⋊ Dic3 |
| Hall | C3×C52 ⋊ #4223 |
| Sylow | C41 ⋊ C52×Dic3 |
| Sylow | C3 ⋊ C52×#4223 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | C3⋊#4223 |
| commutator, hypocenter | C3×C41 | C4×C52 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C41 | C4 |
| prime radical | C3×C52×D41 | C2 |
| cosocle | C3×D41 | C2×C52 |
| LCS | G ▷ C3×C41 | |
| UCS | C1 ◁ C52 | |
96 conjugacy classes of subgroups.
900 conjugacy classes — view the full character table.
| maximal subgroup of | C52×C9⋊#4223, C52⋊C3×C3⋊#4223, C3×C52×C3⋊#4223, … |
| maximal normal subgroup of | C52⋊C3×C3⋊#4223, C3×C52×C3⋊#4223 |
| maximal quotient of | C52×C9⋊#4223, C3×C52×C3⋊#4223, C52×C3⋊(C3⋊#4223) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12300, 147);