Finite Group DatabasebetaFinite Group Databasebeta| order | 3712 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C29×#550 ⋊ C2 |
| Sylow | C29 ⋊ D4×#41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D29 |
| commutator, socle, cosocle | C22×C29 | C25 |
| Fitting | C29×#550 | C2 |
| hypercenter | #550 | D29 |
| hypocenter | C29 | D4×#41 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C22 ◁ #550 | |
1648 conjugacy classes of subgroups.
| transitive degree | μt(G) = 928 |
Polycyclic presentation:
2^7,29|e^2=f,b^a=bf,c^a=cg,d^b=df,h^b=h^28,h^c=h^28,h^d=h^28,h^e=h^28400 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3712, 18000);