Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C32×#106 ⋊ C22 |
| Sylow | C32 ⋊ #2145 |
477 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^7,3^2|a^2=e,c^2=g,d^2=f,f^2=g,b^a=bd,d^a=df,f^a=fg,d^b=dfg,e^b=eg,f^b=fg,h^b=h^2,i^b=i^2,i^c=hi^290 conjugacy classes — view the full character table.
| maximal subgroup of | #72222760, #72222762, #72222789, … |
| maximal normal subgroup of | #72222760, #72222762, #72222789, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 30867);