Finite Group DatabasebetaFinite Group Databasebeta| order | 12300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×D1025 |
| unambiguous semidirect product | (C2×C25)⋊(C3×D41) |
| unambiguous semidirect product | (C2×C41)⋊(C3×D25) |
| Fitting | C2×C3×C25×C41 ⋊ C2 |
| derived, Hall | C25×C41 ⋊ C22×C3 |
| Hall | C3×C25×C41 ⋊ C22 |
| Hall | C3×C41 ⋊ C2×D25 |
| Hall | C3×C25 ⋊ C2×D41 |
| Sylow | C41 ⋊ C2×C3×D25 |
| Sylow | C25 ⋊ C2×C3×D41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D1025 |
| commutator, cosocle, hypocenter | C25×C41 | C22×C3 |
| Frattini | C5 | C2×C3×D205 |
| Fitting | C2×C3×C25×C41 | C2 |
| socle | C2×C3×C5×C41 | D5 |
| LCS | G ▷ C25×C41 | |
| UCS | C1 ◁ C2×C3 | |
60 conjugacy classes of subgroups.
3084 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C9×D1025, C3×D3×D1025, C2×C3×D3075, … |
| maximal normal subgroup of | C2×C9×D1025, C2×C32×D1025 |
| maximal quotient of | C2×C9×D1025, C3×D3×D1025, C2×C3×D3075, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12300, 46);