Finite Group DatabasebetaFinite Group Databasebeta| order | 29196 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #20300457⋊C4 |
| derived, Sylow | C811 ⋊ C4×C9 |
| Hall | #20300457 ⋊ C4 |
| Hall | Dic811 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | D811⋊C3 |
| commutator, hypocenter | C811 | C4×C9 |
| Fitting, socle, prime radical, cosocle | C2×C3×C811 | C2×C3 |
| LCS | G ▷ C811 | |
| UCS | C1 ◁ C2×C3 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 29196 |
Polycyclic presentation:
2,3,811,2,3|a^2=d,b^3=e,c^a=c^810,c^b=c^680846 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29196, 2);