Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2 |
| direct product | C3×(C5⋊AGL(1,𝔽11))⋊D11 |
| unambiguous semidirect product | (C5⋊AGL(1,𝔽11))⋊(C3×D11) |
| unambiguous semidirect product | ((C11⋊C5)⋊D11)⋊(C3×D5) |
| Fitting, socle | C3×C5×C112 ⋊ C22×C5 |
| derived | C5×C112 ⋊ C22×C3×C5 |
| Hall | C3×C5×C11×C11⋊C5 ⋊ C22 |
| Hall | C5×C11×C11⋊C5 ⋊ C22×C3 |
| Hall | C3×C112 ⋊ C2×C5×D5 |
| Sylow | C112 ⋊ C2×C3×C5×D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | (C5⋊AGL(1,𝔽11))⋊D11 |
| commutator, cosocle, hypocenter | C5×C112 | C22×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C112 | C22×C5 |
| LCS | G ▷ C5×C112 | |
| UCS | C1 ◁ C3 | |
200 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1650 |
507 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 534);