Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C11×#427 ⋊ C2 |
| Sylow | C11 ⋊ #2911 |
492 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 213 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,b^2=e,d^2=g,e^2=g,b^a=be,e^a=eg,c^b=cg,h^c=h^10184 conjugacy classes — view the full character table.
| maximal subgroup of | #14670292, #14670295, #14670343, … |
| maximal normal subgroup of | #14670292, #14670295, #14670343, … |
| maximal quotient of | #14722755, #14722794, #14722804, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13098);