Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C3 |
No aliases for this group.
| Fitting | C32×C4×C22⋊C4 ⋊ C2 |
| Sylow | C32 ⋊ #2392 |
2088 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2^7,3^2|a^2=f,d^2=e,b^a=be,c^a=cf,h^a=h^2,i^a=i^2,c^b=cg,h^b=h^2,i^b=i^2204 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 42406);