Finite Group DatabasebetaFinite Group Databasebeta| order | 3712 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C29 ⋊ #1843 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D29 |
| commutator, socle, prime radical | C23×C29 | C22×C4 |
| Fitting | C29×#376 | C2 |
| cosocle | C22×C4×C29 | C23 |
| hypercenter | #376 | D29 |
| hypocenter | C29 | #1843 |
| LCS | G ▷ C23×C29 ▷ C29 | |
| UCS | C1 ◁ C22×C4 ◁ #376 | |
256 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3712 |
Polycyclic presentation:
2^7,29|a^2=f,b^2=d,c^2=e,f^2=g,b^a=bd,c^a=ce,h^a=h^28,c^b=cg604 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3712, 4664);