Finite Group DatabasebetaFinite Group Databasebeta| order | 36012 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×#26046362 |
| Fitting, socle, Hall | C3×C3001 ⋊ C4 |
| derived, Sylow | C3001 ⋊ C3×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #26046362 |
| commutator, hypocenter | C3001 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C3001 | C4 |
| prime radical | C3×D3001 | C2 |
| cosocle | D3001 | C2×C3 |
| LCS | G ▷ C3001 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9003 |
2262 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36012, 10);