Finite Group DatabasebetaFinite Group Databasebeta| order | 3712 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C8×D4×C29 ⋊ C2 |
| Sylow | C29 ⋊ #3302 |
386 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1856 |
Polycyclic presentation:
2^7,29|a^2=e,b^2=g,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^28,d^b=de,f^c=fg,h^c=h^28595 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3712, 16428);