Finite Group DatabasebetaFinite Group Databasebeta| order | 3712 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C82×C29 ⋊ C2 |
| Sylow | C29 ⋊ #1454 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C42 | C22×D29 |
| commutator, socle | C22×C29 | C2×C42 |
| Fitting | C82×C29 | C2 |
| prime radical | C22×D29 | C42 |
| cosocle | C42×C29 | C23 |
| hypercenter | C82 | D29 |
| hypocenter | C29 | #1454 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C42 ◁ C82 | |
178 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1856 |
Polycyclic presentation:
2^7,29|a^2=d,b^2=e,d^2=f,e^2=g,c^a=cfg,c^b=cf,h^c=h^28952 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3712, 2809);