Finite Group DatabasebetaFinite Group Databasebeta| order | 12300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×C3⋊#11717962 |
| unambiguous semidirect product | C3⋊(C5×#11717962) |
| Fitting, socle, Hall | C3×C52×C41 ⋊ C4 |
| derived | C3×C5×C41 ⋊ C4×C5 |
| Hall | C52×C41 ⋊ Dic3 |
| Hall | C3×C41 ⋊ C5×AGL(1,𝔽5) |
| Hall | C3×C52 ⋊ #4223 |
| Sylow | C41 ⋊ C5×ΓL(1,𝔽16) |
| Sylow | C52 ⋊ C3⋊#4223 |
| Sylow | C3 ⋊ C5×#11717962 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C3⋊#11717962 |
| commutator, hypocenter | C3×C5×C41 | C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C41 | C4 |
| prime radical | C3×C5×D205 | C2 |
| cosocle | C3×D205 | C2×C5 |
| LCS | G ▷ C3×C5×C41 | |
| UCS | C1 ◁ C5 | |
52 conjugacy classes of subgroups.
795 conjugacy classes — view the full character table.
| maximal subgroup of | C5×C9⋊#11717962, C3×C5×C3⋊#11717962, C5×C3⋊(C3⋊#11717962) |
| maximal normal subgroup of | C3×C5×C3⋊#11717962 |
| maximal quotient of | C5×C9⋊#11717962, C3×C5×C3⋊#11717962, C5×C3⋊(C3⋊#11717962) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12300, 151);