Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C3×C4 |
No aliases for this group.
| Fitting | C32×#532 ⋊ C2 |
| Sylow | C32 ⋊ #3151 |
1968 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^7,3^2|b^2=e,c^2=f,e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^2,i^a=i^2,d^b=dg,h^b=h^2,i^b=i^2144 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3×#3151, #72214235, #72214535, … |
| maximal normal subgroup of | C3⋊D3×#3151, #72214235, #72214535, … |
| maximal quotient of | #72214235 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 108484);