Finite Group DatabasebetaFinite Group Databasebeta| order | 12300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C52 · Schur multiplier (H2) = C2×C5 |
| direct product | C52×D3×D41 |
| Fitting, socle, Hall | C3×C52×C41 ⋊ C22 |
| derived, Hall | C3×C41 ⋊ C22×C52 |
| Hall | C52×C41 ⋊ C2×D3 |
| Hall | C3×C52 ⋊ C2×D41 |
| Sylow | C41 ⋊ C2×C52×D3 |
| Sylow | C3 ⋊ C2×C52×D41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | D3×D41 |
| commutator, cosocle, hypocenter | C3×C41 | C22×C52 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C41 | C22 |
| LCS | G ▷ C3×C41 | |
| UCS | C1 ◁ C52 | |
160 conjugacy classes of subgroups.
1650 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C52×D9×D41, D3×C52⋊C3×D41, C3×C52×D3×D41, … |
| maximal normal subgroup of | D3×C52⋊C3×D41, C3×C52×D3×D41 |
| maximal quotient of | C52×D9×D41, C3×C52×D3×D41, C52×D3×D123, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12300, 148);