Finite Group DatabasebetaFinite Group Databasebeta| order | 34688 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C26×C42 |
| direct product | C2×#31774639 |
| Fitting | C2×#124×C271 ⋊ C2 |
| Sylow | C271 ⋊ C2×H(3,𝔽4) |
1408 conjugacy classes of subgroups; only the 469 normal subgroups are shown.
This group has 1408 conjugacy classes of subgroups — too many to draw. Only its 469 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 8672 |
3818 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34688, 18630);