Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C4×C11×C16 ⋊ C2 |
| Sylow | C11 ⋊ #2108 |
184 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=d,b^2=e,d^2=f,f^2=g,c^b=cg,h^c=h^10400 conjugacy classes — view the full character table.
| maximal subgroup of | #14665430, #14665434, #14673951, … |
| maximal normal subgroup of | #14665430, #14665434, #14673951, … |
| maximal quotient of | #14662753, #14662761, C16×#4313, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 6105);