Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C32 ⋊ #1790 |
1483 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^7,3^2|a^2=f,b^a=bd,c^a=ce,d^a=dg,i^a=hi^2,e^b=eg,f^b=fg,d^c=dg,h^c=h^2,i^c=h^2i108 conjugacy classes — view the full character table.
| maximal subgroup of | #72252266, #72252270, #72252278, … |
| maximal normal subgroup of | #72252266, #72252270, #72252278, … |
| maximal quotient of | #72252317, #72252374 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 18836);