Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C32×C4×D4 ⋊ C22 |
| Sylow | C32 ⋊ C2×#518 |
4053 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^7,3^2|a^2=g,b^a=bf,d^a=df,c^b=cf,i^d=hi^2,h^e=h^2,i^e=i^2156 conjugacy classes — view the full character table.
| maximal subgroup of | #72222718, C4×#10596675, #72227392, … |
| maximal normal subgroup of | #72222718, C4×#10596675, #72227392, … |
| maximal quotient of | #72260182 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 134019);