Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#27130856 |
| derived | C3×C5×C112 ⋊ C4×C5 |
| Hall | C3×C5×#10597244 ⋊ C4 |
| Hall | C5×#10597244 ⋊ Dic3 |
| Hall | C3×C112 ⋊ C5×Dic5 |
| Sylow | C112 ⋊ C5×Dic15 |
| Sylow | C3 ⋊ #27130856 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊(C5⋊#11925897) |
| commutator, hypocenter | C3×C5×C112 | C4×C5 |
| Fitting, socle, cosocle | C2×C3×C5×C112 | C2×C5 |
| prime radical | C2×C3×C5×#10597244 | C2 |
| LCS | G ▷ C3×C5×C112 | |
| UCS | C1 ◁ C2 | |
136 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 43 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 3300 |
Polycyclic presentation:
2,5,3,5,11^2,2|a^2=g,c^a=c^2,d^a=d^4,e^a=e^10,e^b=e^4,f^b=f^9456 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 409);