Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Fitting | C32×#322 ⋊ C2 |
| Sylow | C32 ⋊ #1336 |
288 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^7,3^2|a^2=d,c^2=e,d^2=f,e^2=g,f^2=g,b^a=bc,c^a=ce,e^a=eg,h^a=h^2,i^a=i^2,c^b=ceg,d^b=dg,e^b=eg,h^b=h^2,i^b=i^2192 conjugacy classes — view the full character table.
| maximal subgroup of | #72255420, C3⋊D3×#1336, #72255423 |
| maximal normal subgroup of | #72255420, C3⋊D3×#1336, #72255423 |
| maximal quotient of | #72269806 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 5672);