Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C32 ⋊ #2121 |
665 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^7,3^2|a^2=e,b^a=bd,d^a=df,f^a=fg,h^a=h^2,i^a=i^2,c^b=cg,e^b=ef,i^b=hi^2,e^d=eg87 conjugacy classes — view the full character table.
| maximal subgroup of | #72252322, #72252325, #72252329, … |
| maximal normal subgroup of | #72252322, #72252325, #72252329, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 30256);