Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C11×H(5,𝔽2) ⋊ C2 |
| Sylow | C11 ⋊ #3019 |
762 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 762 conjugacy classes of subgroups — too many to draw. Only its 161 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 176 |
Polycyclic presentation:
2^7,11|e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,h^a=h^10,e^b=eg,f^b=fg,e^c=eg199 conjugacy classes — view the full character table.
| maximal subgroup of | #14785063, #14785067, #14785074, … |
| maximal normal subgroup of | #14785063, #14785067, #14785074, … |
| maximal quotient of | #14726143, #14726150, #14726182, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13867);