Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C32 ⋊ #1867 |
865 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^7,3^2|a^2=f,b^2=f,b^a=bd,c^a=ce,h^a=h^2,i^a=i^2,e^b=eg,d^c=dg,i^c=hi^2108 conjugacy classes — view the full character table.
| maximal subgroup of | #72260305, C4×#10591531 |
| maximal normal subgroup of | #72260305, C4×#10591531 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 21085);