Finite Group DatabasebetaFinite Group Databasebeta| order | 16064 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | #127×C251 ⋊ C2 |
| Sylow | C251 ⋊ D42 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D251 |
| commutator, socle, cosocle | C22×C251 | C24 |
| Fitting | #127×C251 | C2 |
| hypercenter | #127 | D251 |
| hypocenter | C251 | D42 |
| LCS | G ▷ C22×C251 ▷ C251 | |
| UCS | C1 ◁ C22 ◁ #127 | |
428 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4016 |
Polycyclic presentation:
2^6,251|b^a=be,c^a=cf,d^b=de,g^b=g^250,g^c=g^250,g^d=g^2501775 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44549417, #44549420, #44549479, … |
| maximal normal subgroup of | #44549417, #44549420, #44549479, … |
| maximal quotient of | #44553186, #44553265, #44553346, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16064, 1184);