Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C16 · Schur multiplier (H2) = C43 |
| direct product | C4×#64408⋊C16 |
| unambiguous semidirect product | #64408⋊(C4×C16) |
| derived, Sylow | C73 ⋊ C42×C16 |
558 conjugacy classes of subgroups; only the 301 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 301 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4672 |
544 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1117615);