Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C32×C4⋊C4 ⋊ D4 |
| Sylow | C32 ⋊ #2443 |
1054 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^7,3^2|b^2=f,c^2=f,b^a=be,c^a=cf,d^a=de,i^a=hi^2,c^b=cg,h^b=hi,i^b=i^2,h^d=hi,i^d=i^2,h^e=h^2,i^e=i^272 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 46952);