Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C11 ⋊ #3215 |
400 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 113 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=g,b^2=e,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ceg,h^b=h^10,f^c=fg121 conjugacy classes — view the full character table.
| maximal subgroup of | #14728021, #14728023, #14728030, … |
| maximal normal subgroup of | #14728021, #14728023, #14728030, … |
| maximal quotient of | #14763109, #14763498, #14764323, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 15510);