Finite Group DatabasebetaFinite Group Databasebeta| order | 36972 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×C22⋊#15690493 |
| unambiguous semidirect product | (C22×C3)⋊#15690493 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C22⋊#15690493 |
| commutator, cosocle, hypocenter | C22×C13×C79 | C32 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C13×C79 | C3 |
| LCS | G ▷ C22×C13×C79 | |
| UCS | C1 ◁ C3 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12324 |
4116 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36972, 297);