Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24×C3 |
No aliases for this group.
| Fitting | C2×C32×M16 ⋊ C4 |
| Sylow | C32 ⋊ #1742 |
686 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^7,3^2|a^2=e,b^2=f,c^2=g,e^2=g,b^a=bd,d^a=dg,e^b=eg,h^b=hi,i^b=hi^2,h^f=h^2,i^f=i^284 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 17428);