Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#22625050 |
| Fitting | C2×H(5,𝔽2)×C73 ⋊ C4 |
| Sylow | C73 ⋊ C2×#1402 |
564 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2336 |
646 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1097831);