Finite Group DatabasebetaFinite Group Databasebeta| order | 3712 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C29 ⋊ #2258 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C22×#1181 |
| commutator, socle | C2×C29 | C22×C16 |
| Fitting | C29×M32 | C4 |
| prime radical | #90805 | C8 |
| cosocle | #90768 | C23 |
| hypercenter | M32 | #1181 |
| hypocenter | C29 | #2258 |
| LCS | G ▷ C2×C29 ▷ C29 | |
| UCS | C1 ◁ C8 ◁ M32 | |
106 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1856 |
Polycyclic presentation:
2^7,29|a^2=d,d^2=e,e^2=f,f^2=g,h^a=h^12,c^b=cg,h^b=h^28,h^d=h^28220 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3712, 20934);