Finite Group DatabasebetaFinite Group Databasebeta| order | 16064 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | H(5,𝔽2)×D251 |
| Fitting | H(5,𝔽2)×C251 ⋊ C2 |
| Sylow | C251 ⋊ C2×H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C24×D251 |
| commutator, socle, cosocle | C2×C251 | C25 |
| Fitting | H(5,𝔽2)×C251 | C2 |
| hypercenter | H(5,𝔽2) | D251 |
| hypocenter | C251 | C2×H(5,𝔽2) |
| LCS | G ▷ C2×C251 ▷ C251 | |
| UCS | C1 ◁ C2 ◁ H(5,𝔽2) | |
898 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2008 |
2159 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #453×D251, #455×D251, #44559719, … |
| maximal normal subgroup of | #453×D251, #455×D251, #44559719, … |
| maximal quotient of | #518×D251, #520×D251, #44563569, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16064, 1378);