Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C11×#495 ⋊ C2 |
| Sylow | C11 ⋊ #3285 |
482 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 123 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=g,d^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,d^b=de,e^b=eg,h^b=h^10,h^c=h^10,e^d=eg,h^d=h^10145 conjugacy classes — view the full character table.
| maximal subgroup of | #14910245, #14910252, #14910305, … |
| maximal normal subgroup of | #14910245, #14910252, #14910305, … |
| maximal quotient of | #14744319, #14744334, #14744349, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 16250);