Finite Group DatabasebetaFinite Group Databasebeta| order | 12300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C5 |
| direct product | C52⋊C3×#4223 |
| unambiguous semidirect product | (C52×#4223)⋊C3 |
| Fitting, socle, derived, Hall | C52×C41 ⋊ C3×C4 |
| Hall | C52×#4223 ⋊ C3 |
| Hall | C41×C52⋊C3 ⋊ C4 |
| Sylow | C41 ⋊ C4×C52⋊C3 |
| Sylow | C52 ⋊ C3×#4223 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C41 | C3×C4 |
| prime radical | C52⋊C3×D41 | C2 |
| cosocle | C52×D41 | C2×C3 |
| LCS | G ▷ C52×C41 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
154 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C52⋊C3×#4223, C52⋊C3×C3⋊#4223 |
| maximal normal subgroup of | C3×C52⋊C3×#4223 |
| maximal quotient of | #4223×C52⋊C9, C3×C52⋊C3×#4223, C52⋊C3×C3⋊#4223 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12300, 110);