Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C11×#120 ⋊ C2 |
| Sylow | C11 ⋊ #2021 |
638 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 638 conjugacy classes of subgroups — too many to draw. Only its 75 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|b^a=bd,c^a=ce,f^a=fg,c^b=cf,d^c=dg,h^c=h^10166 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#2021, C2×#13069739, #14781013, … |
| maximal normal subgroup of | D11×#2021, C2×#13069739, #14781013, … |
| maximal quotient of | #14653966, #14653969, #14653973, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 5633);