Finite Group DatabasebetaFinite Group Databasebeta| order | 16064 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#22548763 |
| Fitting | C22×Q8×C251 ⋊ C2 |
| Sylow | C251 ⋊ C2×2−1+4 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C23×D251 |
| commutator, cosocle | C2×C251 | C25 |
| Frattini | C2 | C24×D251 |
| Fitting | C22×Q8×C251 | C2 |
| socle | C22×C251 | C24 |
| hypercenter | C22×Q8 | D251 |
| hypocenter | C251 | C2×2−1+4 |
| LCS | G ▷ C2×C251 ▷ C251 | |
| UCS | C1 ◁ C22 ◁ C22×Q8 | |
794 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8032 |
2534 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44550323, #44550326, #44550337, … |
| maximal normal subgroup of | #44550323, #44550326, #44550337, … |
| maximal quotient of | C2×#30632163, C2×#30632165, C2×#30632168, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16064, 1383);