Finite Group DatabasebetaFinite Group Databasebeta| order | 29156 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C37 · Schur multiplier (H2) = C1 |
| direct product | C37×#11716161 |
| Fitting, socle, Hall | C37×C197 ⋊ C4 |
| derived, Sylow | C197 ⋊ C4×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37 | #11716161 |
| commutator, hypocenter | C197 | C4×C37 |
| Frattini | C1 | G |
| Fitting, socle | C37×C197 | C4 |
| prime radical | C37×D197 | C2 |
| cosocle | D197 | C2×C37 |
| LCS | G ▷ C197 | |
| UCS | C1 ◁ C37 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7289 |
1961 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29156, 6);