Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C9×#486 ⋊ C2 |
| Sylow | C9 ⋊ #3184 |
669 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 669 conjugacy classes of subgroups — too many to draw. Only its 150 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|c^2=fg,d^2=e,f^2=g,h^3=i,b^a=be,c^a=cf,f^a=fg,c^b=cg,h^b=h^2i^2,i^b=i^2,d^c=dg,h^c=h^2i^2,i^c=i^2,h^d=h^2i^2,i^d=i^2120 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#3184, #72244462, #72244500, … |
| maximal normal subgroup of | D9×#3184, #72244462, #72244500, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 110982);