Finite Group DatabasebetaFinite Group Databasebeta| order | 16064 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #95×C251 ⋊ C2 |
| Sylow | C251 ⋊ #386 |
286 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 8032 |
Polycyclic presentation:
2^6,251|a^2=f,b^2=df,b^a=bd,c^a=ce,g^b=g^250,g^c=g^2502528 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #386×D251, C2×#30631565, #44552803, … |
| maximal normal subgroup of | #386×D251, C2×#30631565, #44552803, … |
| maximal quotient of | (C2×D251)⋊#95, #44548599, #44548601, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16064, 427);