Finite Group DatabasebetaFinite Group Databasebeta| order | 12300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C25 · Schur multiplier (H2) = C2 |
| derived, Hall | C22×C41 ⋊ C3×C25 |
| Hall | C22×C41⋊C25 ⋊ C3 |
| Hall | A4×C41 ⋊ C25 |
| Sylow | C41 ⋊ A4×C25 |
| Sylow | C22 ⋊ C3×C41⋊C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | A4×C41⋊C5 |
| commutator, hypocenter | C22×C41 | C3×C25 |
| Fitting, socle, cosocle | C22×C5×C41 | C3×C5 |
| prime radical | C5×A4×C41 | C5 |
| LCS | G ▷ C22×C41 | |
| UCS | C1 ◁ C5 | |
30 conjugacy classes of subgroups.
260 conjugacy classes — view the full character table.
| maximal subgroup of | C3×A4×C41⋊C25 |
| maximal normal subgroup of | C3×A4×C41⋊C25 |
| maximal quotient of | C22⋊C9×C41⋊C25, C3×A4×C41⋊C25 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12300, 17);