Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C32×#117 ⋊ C22 |
| Sylow | C32 ⋊ C4×H(5,𝔽2) |
3475 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^7,3^2|a^2=g,e^2=g,b^a=bf,d^a=df,h^a=h^2,i^a=h^2i,c^b=cf,h^b=h^2,i^b=h^2i,i^d=hi^2,h^e=h^2,i^e=i^2156 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 134198);