Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C32 ⋊ C2×M64 |
273 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 273 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^7,3^2|a^2=d,d^2=e,e^2=f,f^2=g,b^a=bg,i^a=hi^2,h^c=h^2,i^c=i^2192 conjugacy classes — view the full character table.
| maximal subgroup of | #72222480, #72222630, #72222635, … |
| maximal normal subgroup of | #72222480, #72222630, #72222635, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 34479);