Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C11⋊C5×C3⋊(C11⋊AGL(1,𝔽5)) |
| unambiguous semidirect product | C3⋊(C11⋊C5×C11⋊AGL(1,𝔽5)) |
| Fitting, socle, derived | C3×C5×C112 ⋊ C4×C5 |
| Hall | C3×C5×C11×C11⋊C5 ⋊ C4 |
| Hall | C5×C11×C11⋊C5 ⋊ Dic3 |
| Hall | C3×C112 ⋊ C5×AGL(1,𝔽5) |
| Sylow | C112 ⋊ C5×ΓL(1,𝔽16) |
| Sylow | C3 ⋊ C11⋊C5×C11⋊AGL(1,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C5×C112 | C4×C5 |
| prime radical | C3×D5×C11×C11⋊C5 | C2 |
| cosocle | C3×D5×C112 | C2×C5 |
| LCS | G ▷ C3×C5×C112 | |
| UCS | C1 | |
112 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1650 |
483 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 581);