Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C52×C11 · Schur multiplier (H2) = C2×C5 |
| Fitting, socle | C2×C3×C5×C112 ⋊ C2×C5 |
| derived | C3×C11 ⋊ C22×C52×C11 |
| Hall | C3×C5×C11×C11⋊C5 ⋊ C22 |
| Hall | C2×D3×C112 ⋊ C52 |
| Hall | C3×C112 ⋊ C22×C52 |
| Sylow | C112 ⋊ C2×C52×D3 |
| Sylow | C3 ⋊ C22×C5×C11×C11⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5×C11 | D3×C11⋊C5 |
| commutator, cosocle, hypocenter | C3×C11 | C22×C52×C11 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C5×C112 | C2×C5 |
| LCS | G ▷ C3×C11 | |
| UCS | C1 ◁ C2×C5×C11 | |
360 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 140 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1650 |
2310 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 789);