Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C11×#450 ⋊ C2 |
| Sylow | C11 ⋊ #3217 |
490 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 115 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,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,h^a=h^10,c^b=ceg,h^b=h^10,f^c=fg121 conjugacy classes — view the full character table.
| maximal subgroup of | #14728043, #14728045, #14728057, … |
| maximal normal subgroup of | #14728043, #14728045, #14728057, … |
| maximal quotient of | #14763123, #14763507, #14764331, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 15531);