Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Sylow | C9 ⋊ #1437 |
1242 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2^7,3^2|a^2=f,b^2=g,c^2=ef,h^3=i,b^a=bd,c^a=ce,h^b=h^2i^2,i^b=i^2216 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#1437, #72268867, #72268895 |
| maximal normal subgroup of | D9×#1437, #72268867, #72268895 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 7267);