Finite Group DatabasebetaFinite Group Databasebeta| order | 20704 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C24×D647 |
| unambiguous semidirect product | C647⋊C25 |
| unambiguous semidirect product | (C2×C647)⋊C24 |
| Fitting, socle | C24×C647 ⋊ C2 |
| derived, Sylow | C647 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | D647 |
| commutator, cosocle, hypocenter | C647 | C25 |
| Frattini | C1 | G |
| Fitting, socle | C24×C647 | C2 |
| LCS | G ▷ C647 | |
| UCS | C1 ◁ C24 | |
748 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10352 |
5200 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20704, 195);