Finite Group DatabasebetaFinite Group Databasebeta| order | 16064 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C23×C22⋊D251 |
| Fitting | C25×C251 ⋊ C2 |
| Sylow | C251 ⋊ C23×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C2×D251 |
| commutator, cosocle | C2×C251 | C25 |
| Frattini | C2 | C24×D251 |
| Fitting | C25×C251 | C2 |
| socle | C24×C251 | C22 |
| hypercenter | C25 | D251 |
| hypocenter | C251 | C23×D4 |
| LCS | G ▷ C2×C251 ▷ C251 | |
| UCS | C1 ◁ C24 ◁ C25 | |
1362 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8032 |
4040 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44548604, #44550279, C2×#30631563, … |
| maximal normal subgroup of | #44548604, #44550279, C2×#30631563, … |
| maximal quotient of | C23×(C2×D251)⋊C4, C23×C22⋊Dic251, C23×Dic251⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16064, 1370);