Finite Group DatabasebetaFinite Group Databasebeta| order | 13952 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | D4⋊C8×C109 ⋊ C2 |
| Sylow | C109 ⋊ #1635 |
234 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 6976 |
Polycyclic presentation:
2^7,109|a^2=f,b^2=g,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^108,d^b=df,e^b=eg,h^b=h^108,d^c=dg,e^c=eg1538 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13952, 3663);