Finite Group DatabasebetaFinite Group Databasebeta| order | 3712 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C22⋊C4×C29 ⋊ C4 |
| Sylow | C29 ⋊ #1390 |
234 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 928 |
Polycyclic presentation:
2^7,29|a^2=d,b^2=e,b^a=bc,c^a=cf,f^a=fg,h^a=h^12,d^b=df,h^b=h^28,d^c=dg,h^d=h^28166 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3712, 19595);