Finite Group DatabasebetaFinite Group Databasebeta| order | 2624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #103×C41 ⋊ C2 |
| Sylow | C41 ⋊ #452 |
152 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 43 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1312 |
Polycyclic presentation:
2^6,41|a^2=f,c^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^40,d^b=df,g^b=g^40,g^c=g^40299 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2624, 714);