Finite Group DatabasebetaFinite Group Databasebeta| order | 36540 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×D45⋊D29 |
| unambiguous semidirect product | D45⋊(C7×D29) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D45⋊D29 |
| commutator, cosocle, hypocenter | C5×C9×C29 | C22×C7 |
| Frattini | C3 | C7×D15⋊D29 |
| Fitting | C5×C7×C9×C29 | C22 |
| socle | C3×C5×C7×C29 | C2×D3 |
| LCS | G ▷ C5×C9×C29 | |
| UCS | C1 ◁ C7 | |
120 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 120 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) = 9135 |
2520 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36540, 134);