Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C4×D4×C9 ⋊ C2 |
| Sylow | C9 ⋊ #2444 |
915 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2^7,3^2|b^2=ef,c^2=f,h^3=i,b^a=be,c^a=cf,d^a=de,c^b=cg,h^c=h^2i^2,i^c=i^2198 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 46956);