Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C23×#536 ⋊ C2 |
| Sylow | C23 ⋊ #3028 |
716 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 145 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 736 |
Polycyclic presentation:
2^7,23|a^2=g,d^2=g,b^a=be,c^a=cf,d^a=dg,f^b=fg,e^c=eg,h^c=h^22271 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 13915);