Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C11 ⋊ #1280 |
264 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 93 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=g,b^a=bc,c^a=cf,d^b=df,h^b=h^10244 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#1280, C2×#13066458, #14643362, … |
| maximal normal subgroup of | D11×#1280, C2×#13066458, #14643362, … |
| maximal quotient of | #14640302, #14640304, #14640310, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 2352);