Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C11×#362 ⋊ C2 |
| Sylow | C11 ⋊ #2239 |
124 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^7,11|a^2=g,c^2=df,e^2=fg,f^2=g,b^a=bd,c^a=ce,e^a=ef,f^a=fg,e^b=eg,h^b=h^10,d^c=dg,e^c=efg,f^c=fg100 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#2239, C2×#13070834, #14908668, … |
| maximal normal subgroup of | D11×#2239, C2×#13070834, #14908668, … |
| maximal quotient of | #14670102, #14670341, #14670810, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 6728);