Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24×C3×C4 |
No aliases for this group.
| Fitting | C32×#95 ⋊ C4 |
| Sylow | C32 ⋊ #1434 |
898 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 898 conjugacy classes of subgroups — too many to draw. Only its 154 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^7,3^2|a^2=f,b^2=g,c^2=d,b^a=bd,c^a=ce,h^b=hi,i^b=hi^2,h^g=h^2,i^g=i^296 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 7194);