Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C2×C11×#131 ⋊ C2 |
| Sylow | C11 ⋊ #3058 |
524 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 149 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|b^2=eg,e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^10,d^c=dg232 conjugacy classes — view the full character table.
| maximal subgroup of | #14664766, #14664768, #14664774, … |
| maximal normal subgroup of | #14664766, #14664768, #14664774, … |
| maximal quotient of | #14736844, #14736883, #14736931, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 14158);