Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C9×H(5,𝔽2) ⋊ C2 |
| Sylow | C9 ⋊ #3026 |
1200 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 1200 conjugacy classes of subgroups — too many to draw. Only its 216 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^7,3^2|h^3=i,b^a=be,c^a=cf,d^a=dg,h^a=h^2i^2,i^a=i^2,f^b=fg,e^c=eg165 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#3026 |
| maximal normal subgroup of | D9×#3026 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 99346);