Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C2×C32×C22⋊C4 ⋊ C22 |
| Sylow | C32 ⋊ D4×C22⋊C4 |
2647 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^7,3^2|a^2=g,b^a=be,c^a=cf,d^b=de,i^c=hi^2,h^d=h^2,i^d=h^2i138 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 38768);