Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C11×#433 ⋊ C2 |
| Sylow | C11 ⋊ #2977 |
422 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 422 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) = 352 |
Polycyclic presentation:
2^7,11|a^2=f,f^2=g,b^a=be,d^a=de,c^b=ceg,d^b=dg,h^b=h^10,h^c=h^10190 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#2977, C2×#13077671, #15618571, … |
| maximal normal subgroup of | D11×#2977, C2×#13077671, #15618571, … |
| maximal quotient of | #14752472, #14752483, #14752540, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13565);