Finite Group DatabasebetaFinite Group Databasebeta| order | 3712 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C29 ⋊ #2380 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D29 |
| commutator | C22×C29 | C23×C4 |
| Fitting, prime radical | C2×C29×#127 | C2 |
| socle, cosocle | C23×C29 | C24 |
| hypercenter | C2×#127 | D29 |
| hypocenter | C29 | #2380 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C23 ◁ C2×#127 | |
648 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1856 |
Polycyclic presentation:
2^7,29|a^2=g,c^2=ef,d^2=e,b^a=be,c^a=cf,d^a=def,h^a=h^28,c^b=cef,d^b=de430 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3712, 7687);