Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C11 ⋊ #1378 |
132 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^7,11|a^2=d,b^2=e,d^2=f,f^2=g,b^a=bc,e^a=eg,h^a=h^10,c^b=cg,h^b=h^10244 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#1378, C2×#13066703, #14668797, … |
| maximal normal subgroup of | D11×#1378, C2×#13066703, #14668797, … |
| maximal quotient of | #14640610, #14640620, #14640627, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 2597);