Finite Group DatabasebetaFinite Group Databasebeta| order | 1056 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C11 ⋊ AGL(1,ℤ/8) |
| Sylow | C11 ⋊ #914 |
| Sylow | C3 ⋊ #66985 |
136 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 264 |
Polycyclic presentation:
2^5,3,11|a^2=e,b^2=e,d^2=e,c^a=cd,d^a=de,g^a=g^10,c^b=ce,f^b=f^2,d^c=de93 conjugacy classes — view the full character table.
| maximal subgroup of | #72217002, #72217271, D11×#914, … |
| maximal normal subgroup of | #72217002, #72217271, D11×#914, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1056, 483);