Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C32 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×#64408⋊C32 |
| unambiguous semidirect product | #64408⋊(C2×C32) |
| derived, Sylow | C73 ⋊ C2×C4×C32 |
270 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 149 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, 1117961);