Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | #344×C89 ⋊ C2 |
| Sylow | C89 ⋊ #1757 |
284 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,89|a^2=e,b^2=f,c^2=e,e^2=g,b^a=bd,f^a=fg,d^b=dg,h^c=h^881012 conjugacy classes — view the full character table.
| maximal subgroup of | #1757×D89, C2×#26020051, #36552130, … |
| maximal normal subgroup of | #1757×D89, C2×#26020051, #36552130, … |
| maximal quotient of | #36444955, #36444959, #36444963, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 4309);