Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29×C3 |
No aliases for this group.
| Sylow | C32 ⋊ C2×#568 |
2350 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^7,3^2|a^2=f,f^2=g,d^a=dg,h^a=hi,i^a=hi^2,c^b=cg,h^e=h^2,i^e=i^2,h^f=h^2,i^f=i^2108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 152503);