Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Fitting | C32×M64 ⋊ C2 |
| Sylow | C32 ⋊ #2263 |
336 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^7,3^2|d^2=ef,e^2=fg,f^2=g,b^a=bd,c^a=cg,d^a=de,e^a=ef,f^a=fg,h^a=h^2,i^a=i^2,d^b=de,e^b=ef,f^b=fg,h^b=h^2,i^b=i^2186 conjugacy classes — view the full character table.
| maximal subgroup of | #72254892, C3⋊D3×#2263, #72255432 |
| maximal normal subgroup of | #72254892, C3⋊D3×#2263, #72255432 |
| maximal quotient of | #72254882 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 34604);