Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C32×C42 ⋊ C22 |
| Sylow | C32 ⋊ #1789 |
1365 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 1365 conjugacy classes of subgroups — too many to draw. Only its 156 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^7,3^2|a^2=f,d^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,i^a=hi^2,d^b=dg,i^b=hi^2,h^c=h^2,i^c=i^2126 conjugacy classes — view the full character table.
| maximal subgroup of | #72252262, #72252271, #72252273 |
| maximal normal subgroup of | #72252262, #72252271, #72252273 |
| maximal quotient of | #72252311, #72252312 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 18816);