Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C22×C3×C42 |
No aliases for this group.
| Fitting | C32×#120 ⋊ C4 |
| Sylow | C32 ⋊ #2375 |
1350 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 1350 conjugacy classes of subgroups — too many to draw. Only its 152 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^7,3^2|a^2=g,b^a=be,c^a=cf,d^a=def,h^a=hi,i^a=hi^2,c^b=cef,d^b=de,h^g=h^2,i^g=i^266 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 41603);