Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C3 |
No aliases for this group.
| Fitting | C2×C32×#41 ⋊ C4 |
| Sylow | C32 ⋊ C2×#421 |
1662 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^7,3^2|a^2=f,e^2=g,f^2=g,b^a=be,c^a=cg,e^a=eg,h^a=hi,i^a=hi^2,e^b=eg,h^d=h^2,i^d=i^2,h^f=h^2,i^f=i^284 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 92160);