Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C32 ⋊ #2010 |
835 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^7,3^2|d^2=g,b^a=bd,c^a=ce,d^a=dg,f^a=fg,h^a=h^2,i^a=h^2i,c^b=cf,d^b=dg,e^b=eg,i^b=hi^2,h^c=h^2,i^c=h^2i96 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 26428);