Finite Group DatabasebetaFinite Group Databasebeta| order | 20744 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×#23780505 |
| unambiguous semidirect product | D2593⋊C4 |
| Fitting, socle | C2×C2593 ⋊ C4 |
| derived, Sylow | C2593 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #23780505 |
| commutator, hypocenter | C2593 | C2×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C2593 | C4 |
| prime radical | C2×D2593 | C2 |
| cosocle | D2593 | C22 |
| LCS | G ▷ C2593 | |
| UCS | C1 ◁ C2 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5186 |
1304 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20744, 14);