Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C22×C11×C22⋊C4 ⋊ C2 |
| Sylow | C11 ⋊ #2411 |
786 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 165 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=f,b^2=e,b^a=be,c^a=cf,d^a=de,h^a=h^10,c^b=cg238 conjugacy classes — view the full character table.
| maximal subgroup of | #14791133, #14791137, #14806922, … |
| maximal normal subgroup of | #14791133, #14791137, #14806922, … |
| maximal quotient of | #14675650, #14676504, #14676589, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 7895);