Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C3×C4 |
No aliases for this group.
| Fitting | C32×#390 ⋊ C2 |
| Sylow | C32 ⋊ #2377 |
1728 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2^7,3^2|a^2=g,d^2=e,b^a=be,c^a=cf,d^a=def,c^b=cef,d^b=de,h^d=h^2,i^d=i^2150 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 41713);