Finite Group DatabasebetaFinite Group Databasebeta| order | 11700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×D13×D75 |
| Fitting, Hall | C32×C13×C25 ⋊ C22 |
| derived | C3×C13×C25 ⋊ C22×C3 |
| Hall | C13×C25 ⋊ C2×C3×D3 |
| Hall | C32×C25 ⋊ C2×D13 |
| Hall | C32×C13 ⋊ C2×D25 |
| Sylow | C25 ⋊ C3×D3×D13 |
| Sylow | C13 ⋊ C2×C3×D75 |
| Sylow | C32 ⋊ D13×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D13×D75 |
| commutator, cosocle, hypocenter | C3×C13×C25 | C22×C3 |
| Frattini | C5 | C3×D13×D15 |
| Fitting | C32×C13×C25 | C22 |
| socle | C32×C5×C13 | C2×D5 |
| LCS | G ▷ C3×C13×C25 | |
| UCS | C1 ◁ C3 | |
132 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
936 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11700, 143);