Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Fitting | C32×M64 ⋊ C2 |
| Sylow | C32 ⋊ #1419 |
234 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^7,3^2|a^2=d,c^2=efg,d^2=g,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,c^b=ceg,d^b=dg,e^b=ef,f^b=fg,h^b=h^2,i^b=i^2186 conjugacy classes — view the full character table.
| maximal subgroup of | #72254892, C3⋊D3×#1419, #72255439 |
| maximal normal subgroup of | #72254892, C3⋊D3×#1419, #72255439 |
| maximal quotient of | #72254884 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 6991);