Finite Group DatabasebetaFinite Group Databasebeta| order | 20576 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C24×D643 |
| unambiguous semidirect product | C643⋊C25 |
| unambiguous semidirect product | (C2×C643)⋊C24 |
| Fitting, socle | C24×C643 ⋊ C2 |
| derived, Sylow | C643 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | D643 |
| commutator, cosocle, hypocenter | C643 | C25 |
| Frattini | C1 | G |
| Fitting, socle | C24×C643 | C2 |
| LCS | G ▷ C643 | |
| UCS | C1 ◁ C24 | |
748 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10288 |
5168 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20576, 195);