Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C32×#99 ⋊ C22 |
| Sylow | C32 ⋊ C2×#458 |
1693 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 1693 conjugacy classes of subgroups — too many to draw. Only its 174 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^7,3^2|a^2=g,b^a=be,c^a=cf,i^a=hi^2,f^b=fg,e^c=eg,i^c=hi^2,h^d=h^2,i^d=i^275 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 99294);