Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C22⋊C8×C89 ⋊ C2 |
| Sylow | C89 ⋊ #1780 |
612 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 117 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,f^2=g,b^a=bd,c^a=ce,c^b=cg,h^c=h^881804 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36441054, #36446601, #36446610, … |
| maximal normal subgroup of | #36441054, #36446601, #36446610, … |
| maximal quotient of | #36445773, #36445774, #36445775, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 4421);