Finite Group DatabasebetaFinite Group Databasebeta| order | 26176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×D4×C409 ⋊ C4 |
| Sylow | C409 ⋊ #386 |
286 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 3272 |
Polycyclic presentation:
2^6,409|a^2=f,b^2=df,b^a=bd,c^a=ce,g^a=g^266,g^b=g^143,g^f=g^4081048 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26176, 1497);