Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C3 |
No aliases for this group.
| Fitting | C32×#126 ⋊ C4 |
| Sylow | C32 ⋊ #2373 |
742 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^7,3^2|a^2=g,b^2=g,c^2=e,d^2=ef,b^a=be,c^a=cf,h^a=h^2i^2,i^a=h^2i,d^b=de,h^b=hi,i^b=hi^2,h^g=h^2,i^g=i^278 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 41397);