Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | D4×Q8×C11 ⋊ C2 |
| Sylow | C11 ⋊ #3329 |
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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=eg,b^2=g,c^2=g,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,h^a=h^10,c^b=cg,d^b=de,f^c=fg154 conjugacy classes — view the full character table.
| maximal subgroup of | #14743491, #14743493, #14743551, … |
| maximal normal subgroup of | #14743491, #14743493, #14743551, … |
| maximal quotient of | #14769414, #14770227, #14771103, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 16804);