Finite Group DatabasebetaFinite Group Databasebeta| order | 3712 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C29×#387 ⋊ C2 |
| Sylow | C29 ⋊ #2376 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D29 |
| commutator | C22×C29 | C23×C4 |
| Fitting | C29×#387 | C2 |
| socle, cosocle | C23×C29 | C24 |
| prime radical | C22×D116 | C22 |
| hypercenter | #387 | D29 |
| hypocenter | C29 | #2376 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C23 ◁ #387 | |
512 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1856 |
Polycyclic presentation:
2^7,29|a^2=g,c^2=e,b^a=be,c^a=cf,d^a=def,c^b=cef,d^b=de,h^b=h^28,h^c=h^28,h^d=h^28430 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3712, 7657);