Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C32×#121 ⋊ C22 |
| Sylow | C32 ⋊ C2×#469 |
1405 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^7,3^2|b^2=eg,e^2=g,b^a=be,c^a=cf,e^a=eg,c^b=cg,i^b=hi^2,h^d=h^2,i^d=i^278 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 100978);