Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of PSU(3,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Sylow | C32 ⋊ C4⋊C32 |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^7,3^2|a^2=d,b^2=c,d^2=e,e^2=f,f^2=g,b^a=bc,h^a=hi,i^a=hi^2,h^b=i^2,i^b=h,h^c=h^2,i^c=i^2,h^d=h^2,i^d=i^296 conjugacy classes — view the full character table.
| maximal subgroup of | C32×PSU(3,𝔽2), C3×#11773018, #72219114, … |
| maximal normal subgroup of | C32×PSU(3,𝔽2), C3×#11773018, #72219114, … |
| maximal quotient of | C3×#11773018 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 7029);