Finite Group DatabasebetaFinite Group Databasebeta| order | 16064 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C22⋊Q8×C251 ⋊ C2 |
| Sylow | C251 ⋊ #537 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D251 |
| commutator, socle, cosocle | C22×C251 | C24 |
| Fitting | C22⋊Q8×C251 | C2 |
| hypercenter | C22⋊Q8 | D251 |
| hypocenter | C251 | #537 |
| LCS | G ▷ C22×C251 ▷ C251 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
294 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 103 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|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 | #44559670, #44559673, #44559681, … |
| maximal normal subgroup of | #44559670, #44559673, #44559681, … |
| maximal quotient of | #44552954, #44552956, #44552980, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16064, 1129);