Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #328×C89 ⋊ C2 |
| Sylow | C89 ⋊ #1513 |
286 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 63 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,c^2=g,d^2=g,b^a=bd,c^a=cg,d^a=df,d^b=dg,e^b=efg,h^b=h^88,h^c=h^88862 conjugacy classes — view the full character table.
| maximal subgroup of | #1513×D89, C2×#26018794, #36521696, … |
| maximal normal subgroup of | #1513×D89, C2×#26018794, #36521696, … |
| maximal quotient of | #36442525, #36442527, #36442532, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 3052);