Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C22×C9×C22⋊C4 ⋊ C2 |
| Sylow | C9 ⋊ #1438 |
1752 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2^7,3^2|a^2=g,h^3=i,b^a=bd,c^a=ce,c^b=cf,h^c=h^2i^2,i^c=i^2204 conjugacy classes — view the full character table.
| maximal subgroup of | #72268791, D9×#1438, #72268867, … |
| maximal normal subgroup of | #72268791, D9×#1438, #72268867, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 7282);