Finite Group DatabasebetaFinite Group Databasebeta| order | 16064 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C4×C251⋊C8 |
| derived, Sylow | C251 ⋊ C2×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C42 | D251 |
| commutator, hypocenter | C251 | C2×C4×C8 |
| Frattini | C2×C4 | C22×D251 |
| Fitting | C2×C42×C251 | C2 |
| socle, prime radical | C23×C251 | C2×C4 |
| cosocle | C2×C4×C251 | C23 |
| LCS | G ▷ C251 | |
| UCS | C1 ◁ C2×C42 | |
162 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16064 |
4064 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C251⋊#1273, #44548199, #44548201, … |
| maximal normal subgroup of | C251⋊#1273, #44548199, #44548201, … |
| maximal quotient of | C2×C8×C251⋊C8, C2×#30631408, M16×C251⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16064, 495);