Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
| direct product | #498×D89 |
| Fitting | #498×C89 ⋊ C2 |
| Sylow | C89 ⋊ C2×#498 |
424 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1012 conjugacy classes — view the full character table.
| maximal subgroup of | #1654×D89, #1651×D89, #1653×D89, … |
| maximal normal subgroup of | #1654×D89, #1651×D89, #1653×D89, … |
| maximal quotient of | #1844×D89, #1941×D89, #1990×D89, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 15006);