Finite Group DatabasebetaFinite Group Databasebeta| order | 3712 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Sylow | C29 ⋊ #2317 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D29 |
| commutator | C22×C29 | C23×C4 |
| Fitting | C29×#385 | C2 |
| socle, cosocle | C23×C29 | C24 |
| prime radical | C24×C29 | C23 |
| hypercenter | #385 | D29 |
| hypocenter | C29 | #2317 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C23 ◁ #385 | |
600 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1856 |
Polycyclic presentation:
2^7,29|a^2=g,c^2=f,d^2=e,b^a=be,c^a=cf,d^a=de,c^b=ce,h^d=h^28436 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3712, 7129);