Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C11 ⋊ #2950 |
456 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 221 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|a^2=f,b^2=g,c^2=fg,e^2=g,b^a=be,d^a=dg,e^a=eg,h^a=h^10,e^b=eg,d^c=dg,h^c=h^10184 conjugacy classes — view the full character table.
| maximal subgroup of | #14669894, #14669898, #14670405, … |
| maximal normal subgroup of | #14669894, #14669898, #14670405, … |
| maximal quotient of | #14723247, #14723472, #14723618, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13378);