Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C32 ⋊ #2957 |
956 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^7,3^2|a^2=f,c^2=f,e^2=g,f^2=g,b^a=be,d^a=dg,e^a=eg,h^a=h^2,i^a=h^2i,e^b=eg,d^c=dg,h^c=h^2,i^c=i^2,i^d=hi^2108 conjugacy classes — view the full character table.
| maximal subgroup of | #72222754, #72222766, #72222794, … |
| maximal normal subgroup of | #72222754, #72222766, #72222794, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 95226);