Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C2×C32×C22⋊C4 ⋊ C22 |
| Sylow | C32 ⋊ C2×#551 |
2993 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^7,3^2|a^2=f,b^2=g,b^a=bf,c^a=cg,d^b=df,i^b=hi^2,h^e=h^2,i^e=i^2120 conjugacy classes — view the full character table.
| maximal subgroup of | #72215021, #72215187, #72215208 |
| maximal normal subgroup of | #72215021, #72215187, #72215208 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 136910);