Finite Group DatabasebetaFinite Group Databasebeta| order | 12300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C52 · Schur multiplier (H2) = C2×C5 |
| Fitting, socle | C22×C5×C41 ⋊ C3×C5 |
| derived, Hall | C22×C41 ⋊ C3×C52 |
| Hall | C22×C5×C41⋊C5 ⋊ C3 |
| Hall | A4×C41 ⋊ C52 |
| Sylow | C41 ⋊ C52×A4 |
| Sylow | C22 ⋊ C3×C5×C41⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | A4×C41⋊C5 |
| commutator, cosocle, hypocenter | C22×C41 | C3×C52 |
| Frattini | C1 | G |
| Fitting, socle | C22×C5×C41 | C3×C5 |
| LCS | G ▷ C22×C41 | |
| UCS | C1 ◁ C5 | |
80 conjugacy classes of subgroups.
260 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C5×A4×C41⋊C5 |
| maximal normal subgroup of | C3×C5×A4×C41⋊C5 |
| maximal quotient of | C5×C22⋊C9×C41⋊C5, C3×C5×A4×C41⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12300, 95);