Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C11×#126 ⋊ C2 |
| Sylow | C11 ⋊ #2860 |
516 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 516 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) = 704 |
Polycyclic presentation:
2^7,11|b^2=eg,c^2=f,d^2=e,b^a=be,c^a=cf,d^a=dg,h^c=h^10184 conjugacy classes — view the full character table.
| maximal subgroup of | #14926719, #14926725, #14926742, … |
| maximal normal subgroup of | #14926719, #14926725, #14926742, … |
| maximal quotient of | #14684967, #14685028, #14685039, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 12875);