Finite Group DatabasebetaFinite Group Databasebeta| order | 3392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C22⋊C8×C53 ⋊ C2 |
| Sylow | C53 ⋊ #482 |
106 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1696 |
Polycyclic presentation:
2^6,53|b^2=f,c^2=d,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^52,e^c=ef,g^c=g^52539 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3392, 874);