Finite Group DatabasebetaFinite Group Databasebeta| order | 34596 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C312 · Schur multiplier (H2) = C31 |
| direct product | C312×Dic9 |
| unambiguous semidirect product | C9⋊(C4×C312) |
| derived, Sylow | C9 ⋊ C4×C312 |
| Hall | C9×C312 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C312 | D9 |
| commutator, hypocenter | C9 | C4×C312 |
| Frattini | C2×C3 | D3×C312 |
| Fitting | C2×C9×C312 | C2 |
| socle, prime radical | C2×C3×C312 | D3 |
| cosocle | C2×C9 | C2×C312 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C2×C312 | |
306 conjugacy classes of subgroups.
| transitive degree | μt(G) = 34596 |
11532 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34596, 61);