Finite Group DatabasebetaFinite Group Databasebeta| order | 22144 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×#26012434 |
| unambiguous semidirect product | D173⋊#381 |
| Fitting | C23×C4×C173 ⋊ C4 |
| Sylow | C173 ⋊ C2×#381 |
1144 conjugacy classes of subgroups; only the 258 normal subgroups are shown.
This group has 1144 conjugacy classes of subgroups — too many to draw. Only its 258 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 5536 |
1432 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22144, 20953);