Finite Group DatabasebetaFinite Group Databasebeta| order | 3712 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C29×#123 ⋊ C4 |
| Sylow | C29 ⋊ #2322 |
632 conjugacy classes of subgroups.
| transitive degree | μt(G) = 464 |
Polycyclic presentation:
2^7,29|a^2=g,b^2=g,c^2=e,b^a=be,c^a=cf,d^a=de,h^a=h^17,c^b=ce,h^b=h^12,h^g=h^28142 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3712, 20996);