Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C3×C4 |
No aliases for this group.
| Fitting | C2×C32×#97 ⋊ C2 |
| Sylow | C32 ⋊ #3150 |
1692 conjugacy classes of subgroups; only the 393 normal subgroups are shown.
This group has 1692 conjugacy classes of subgroups — too many to draw. Only its 393 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2^7,3^2|b^2=e,c^2=f,d^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^2,i^a=i^2,c^b=cg192 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 108437);