Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | #431×C89 ⋊ C2 |
| Sylow | C89 ⋊ #1502 |
284 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 89 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=fg,d^2=g,b^a=bd,d^a=df,h^a=h^88,d^b=dg,e^b=efg,h^b=h^881798 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36445492, #36445495, #36445506, … |
| maximal normal subgroup of | #36445492, #36445495, #36445506, … |
| maximal quotient of | #36442365, #36442402, #36442405, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 3006);