Finite Group DatabasebetaFinite Group Databasebeta| order | 36726 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C2×C6121⋊C3 |
| unambiguous semidirect product | (C2×C6121)⋊C3 |
| Fitting, socle, Hall | C2×C6121 ⋊ C3 |
| derived, Sylow | C6121 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C6121⋊C3 |
| commutator, cosocle, hypocenter | C6121 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C6121 | C3 |
| LCS | G ▷ C6121 | |
| UCS | C1 ◁ C2 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12242 |
4086 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36726, 2);