Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C3×C4 |
No aliases for this group.
| Fitting | C32×#442 ⋊ C2 |
| Sylow | C32 ⋊ #3184 |
1338 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2^7,3^2|c^2=fg,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,c^b=cg,h^b=h^2,i^b=i^2,d^c=dg120 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3×#3184, #72219794 |
| maximal normal subgroup of | C3⋊D3×#3184, #72219794 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 110977);