Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C32×#102 ⋊ C22 |
| Sylow | C32 ⋊ C2×#442 |
1317 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^7,3^2|a^2=f,c^2=fg,e^2=g,b^a=be,c^a=cg,e^a=eg,e^b=eg,i^c=hi^2,h^d=h^2,i^d=i^2102 conjugacy classes — view the full character table.
| maximal subgroup of | D32×#442, #72227392, #72228217, … |
| maximal normal subgroup of | D32×#442, #72227392, #72228217 |
| maximal quotient of | #72222843, #72222849, #72222854, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 94167);