Finite Group DatabasebetaFinite Group Databasebeta| order | 21568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×D4×C337 ⋊ C4 |
| Sylow | C337 ⋊ #518 |
338 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2696 |
Polycyclic presentation:
2^6,337|a^2=f,b^a=be,d^a=de,g^a=g^148,c^b=ce,g^f=g^336874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21568, 1616);