Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C32 ⋊ #2110 |
343 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^7,3^2|a^2=d,b^2=e,d^2=f,f^2=g,b^a=bf,e^a=eg,h^a=h^2,i^a=i^2,c^b=cg,d^b=dg,i^c=hi^2126 conjugacy classes — view the full character table.
| maximal subgroup of | #72222742, #72222743, #72222773, … |
| maximal normal subgroup of | #72222742, #72222743, #72222773, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 29955);