Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#24909480 |
| Fitting | C2×H(3,𝔽4)×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#2202 |
1284 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1284 conjugacy classes of subgroups — too many to draw. Only its 171 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2656 |
1592 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 323721);