Finite Group DatabasebetaFinite Group Databasebeta| order | 3712 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C2×C42 |
No aliases for this group.
| Sylow | C29 ⋊ #1726 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×#1181 |
| commutator | C2×C29 | C43 |
| Fitting | C29×#95 | C4 |
| socle, prime radical | C23×C29 | C22×C4 |
| cosocle | C22×Dic29 | C23 |
| hypercenter | #95 | #1181 |
| hypocenter | C29 | #1726 |
| LCS | G ▷ C2×C29 ▷ C29 | |
| UCS | C1 ◁ C23 ◁ #95 | |
328 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3712 |
Polycyclic presentation:
2^7,29|a^2=d,b^2=e,c^2=f,d^2=g,h^a=h^12,c^b=cg,h^d=h^28220 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3712, 20167);