Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Fitting | C2×C32×M16 ⋊ C4 |
| Sylow | C32 ⋊ #1395 |
320 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 40 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,b^2=e,c^2=g,e^2=g,b^a=bc,c^a=cf,e^a=eg,f^a=fg,h^a=hi,i^a=hi^2,d^b=dfg,h^b=h^2,i^b=i^2,d^c=dg,h^d=h^2,i^d=i^266 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 6645);