Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C3×C8 |
No aliases for this group.
| Fitting | C32×C82 ⋊ C2 |
| Sylow | C32 ⋊ #1455 |
642 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2^7,3^2|a^2=d,b^2=e,d^2=f,e^2=g,c^a=cf,c^b=cg,h^c=h^2,i^c=i^2312 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3×#1455, #72214058, #72214125, … |
| maximal normal subgroup of | C3⋊D3×#1455, #72214058, #72214125, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 7699);