Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C32×#106 ⋊ C22 |
| Sylow | C32 ⋊ C2×#427 |
1089 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^7,3^2|a^2=f,b^2=e,c^2=g,e^2=g,b^a=be,e^a=eg,i^c=hi^2,h^d=h^2,i^d=i^2126 conjugacy classes — view the full character table.
| maximal subgroup of | #72222674, #72222711, #72222718, … |
| maximal normal subgroup of | #72222674, #72222711, #72222718, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 92439);