Finite Group DatabasebetaFinite Group Databasebeta| order | 34012 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×#15690586 |
| Fitting, socle, Hall | C11×C773 ⋊ C4 |
| derived, Sylow | C773 ⋊ C4×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | #15690586 |
| commutator, hypocenter | C773 | C4×C11 |
| Frattini | C1 | G |
| Fitting, socle | C11×C773 | C4 |
| prime radical | C11×D773 | C2 |
| cosocle | D773 | C2×C11 |
| LCS | G ▷ C773 | |
| UCS | C1 ◁ C11 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8503 |
2167 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34012, 6);