Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C32×H(5,𝔽2) ⋊ C22 |
| Sylow | C32 ⋊ #3288 |
1057 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^7,3^2|e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,i^a=hi^2,d^b=de,e^b=eg,f^c=fg,e^d=eg,h^d=h^2,i^d=h^2i81 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 120610);