Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26×C3 |
No aliases for this group.
| Fitting | C2×C32×H(5,𝔽2) ⋊ C2 |
| Sylow | C32 ⋊ #3012 |
2292 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^7,3^2|d^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^2,i^a=i^2,e^b=eg,d^c=dg168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 98575);