Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×C32×M16 ⋊ C22 |
| Sylow | C32 ⋊ #3585 |
3077 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^7,3^2|f^2=g,b^a=bf,e^a=eg,f^a=fg,h^a=h^2,i^a=i^2,f^b=fg,h^b=h^2,i^b=i^2,d^c=dg,i^d=hi^2117 conjugacy classes — view the full character table.
| maximal subgroup of | #72213893, #72214293, #72214366, … |
| maximal normal subgroup of | #72213893, #72214293, #72214366, … |
| maximal quotient of | #72222697 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153078);