Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | Q8×#13083551 |
| Fitting | C2×C4×Q8×C89 ⋊ C2 |
| Sylow | C89 ⋊ Q8×C22⋊C4 |
820 conjugacy classes of subgroups; only the 287 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 287 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1810 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36570141, #36570142, #36570171, … |
| maximal normal subgroup of | #36570141, #36570142, #36570171, … |
| maximal quotient of | C4⋊C4×#13083551, Q8×#15667919, #36475969, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 7343);