Finite Group DatabasebetaFinite Group Databasebeta| order | 3712 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C2×C4×D4×C29 ⋊ C2 |
| Sylow | C29 ⋊ #2321 |
808 conjugacy classes of subgroups.
| transitive degree | μt(G) = 928 |
Polycyclic presentation:
2^7,29|a^2=g,b^2=g,b^a=be,c^a=cf,d^a=de,c^b=ce,h^c=h^28604 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3712, 7164);