Finite Group DatabasebetaFinite Group Databasebeta| order | 36036 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D33⋊(ΓL(1,𝔽8)⋊D13) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C7×C11×C13 | C22×C3 |
| LCS | G ▷ C3×C7×C11×C13 | |
| UCS | C1 | |
176 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 3003 |
Polycyclic presentation:
2^2,3^2,7,11,13|e^a=e^6,f^a=f^10,g^a=g^12,d^b=d^2,f^b=f^10,e^c=e^2621 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36036, 426);