Finite Group DatabasebetaFinite Group Databasebeta| order | 1056 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×Q8×C11 ⋊ C22 |
| Hall | C3×C11 ⋊ C2×SD16 |
| Sylow | C11 ⋊ D3×SD16 |
| Sylow | C3 ⋊ SD16×D11 |
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|c^2=e,d^2=e,c^a=cd,d^a=de,g^a=g^10,c^b=cd,d^b=de,f^b=f^2,d^c=de81 conjugacy classes — view the full character table.
| maximal subgroup of | #72217022, #72217361, D3×SD16×D11, … |
| maximal normal subgroup of | #72217022, #72217361, D3×SD16×D11, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1056, 492);