Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C3×C4 |
No aliases for this group.
| Fitting | C32×#405 ⋊ C2 |
| Sylow | C32 ⋊ C4×#131 |
1716 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2^7,3^2|a^2=e,b^2=f,e^2=g,h^b=h^2,i^b=i^2,d^c=dg,h^d=h^2,i^d=i^2240 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 91265);