Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C11 ⋊ #1816 |
264 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=f,b^2=dg,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,h^b=h^10,e^c=eg,f^c=fg142 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#1816, C2×#13068678, #14753455, … |
| maximal normal subgroup of | D11×#1816, C2×#13068678, #14753455, … |
| maximal quotient of | #14646650, #14646655, #14646748, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 4572);