Finite Group DatabasebetaFinite Group Databasebeta| order | 13952 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C109 ⋊ #3363 |
336 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 139 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 13952 |
Polycyclic presentation:
2^7,109|a^2=g,b^2=e,c^2=g,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^108,d^b=de,f^c=fg,h^c=h^1082195 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13952, 17189);