Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of GO+(4,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C32 ⋊ C4⋊C32 |
96 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,i^a=hi^2,h^b=hi,i^b=hi^2,h^c=h^2,i^c=i^2144 conjugacy classes — view the full character table.
| maximal subgroup of | #72219099, C3×#11773017, C32×GO+(4,𝔽2), … |
| maximal normal subgroup of | #72219099, C3×#11773017, C32×GO+(4,𝔽2), … |
| maximal quotient of | C3×#11773017 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 7028);