Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C89 ⋊ #1953 |
184 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 79 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=f,b^2=f,c^2=e,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,d^b=dg,h^c=h^881000 conjugacy classes — view the full character table.
| maximal subgroup of | #1953×D89, C2×#26021039, #36557998, … |
| maximal normal subgroup of | #1953×D89, C2×#26021039, #36557998, … |
| maximal quotient of | #36453036, #36453041, #36453046, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 5297);