Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C32 ⋊ C2×#368 |
337 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 337 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=e,b^2=df,d^2=fg,e^2=g,f^2=g,b^a=bd,d^a=df,f^a=fg,i^a=hi^2,h^c=h^2,i^c=i^2120 conjugacy classes — view the full character table.
| maximal subgroup of | #72222550, #72222635, #72222639 |
| maximal normal subgroup of | #72222550, #72222635, #72222639 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 31268);