Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Sylow | C32 ⋊ #1426 |
156 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^7,3^2|a^2=d,b^2=cef,c^2=efg,e^2=fg,f^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^2,i^a=i^2,d^b=dg,h^b=h^2,i^b=i^2114 conjugacy classes — view the full character table.
| maximal subgroup of | #72255427, C3⋊D3×#1426, #72255434 |
| maximal normal subgroup of | #72255427, C3⋊D3×#1426, #72255434 |
| maximal quotient of | #72254952 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 7085);