Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×#22626958 |
| Fitting | C22×D4×C73 ⋊ C8 |
| Sylow | C73 ⋊ C2×#1318 |
834 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 834 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1168 |
232 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1117128);