Finite Group DatabasebetaFinite Group Databasebeta| order | 16064 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C22⋊Q8×C251 ⋊ C2 |
| Sylow | C251 ⋊ #542 |
216 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 93 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|b^2=ef,d^2=e,b^a=be,c^a=cf,d^a=de,c^b=ce,g^b=g^250,g^c=g^250,g^d=g^2501772 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #542×D251, C2×#30632307, #44563748, … |
| maximal normal subgroup of | #542×D251, C2×#30632307, #44563748, … |
| maximal quotient of | #44552971, #44553007, #44553014, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16064, 1169);