Finite Group DatabasebetaFinite Group Databasebeta| order | 16064 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×#16860810 |
| Fitting | C23×C4×C251 ⋊ C2 |
| Sylow | C251 ⋊ C22×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C2×D251 |
| commutator, cosocle | C2×C251 | C25 |
| Frattini | C2 | C24×D251 |
| Fitting | C23×C4×C251 | C2 |
| socle | C23×C251 | C23 |
| hypercenter | C23×C4 | D251 |
| hypocenter | C251 | C22×#41 |
| LCS | G ▷ C2×C251 ▷ C251 | |
| UCS | C1 ◁ C22×C4 ◁ C23×C4 | |
890 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8032 |
4040 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44550276, #44550282, #44550291, … |
| maximal normal subgroup of | #44550276, #44550282, #44550291, … |
| maximal quotient of | C22×#22548672, C22×#22548674, C22×C4×C22⋊D251, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16064, 1376);