Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | #120×Dic89 |
| Sylow | C89 ⋊ C4×#120 |
1224 conjugacy classes of subgroups; only the 289 normal subgroups are shown.
This group has 1224 conjugacy classes of subgroups — too many to draw. Only its 289 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1288 conjugacy classes. The character table is too large to display.
| maximal subgroup of | AΣL(1,𝔽16)×Dic89, #36470389, B(4,𝔽2)×Dic89, … |
| maximal normal subgroup of | AΣL(1,𝔽16)×Dic89, #36470389, B(4,𝔽2)×Dic89, … |
| maximal quotient of | #386×Dic89, #385×Dic89, #379×Dic89, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 7013);