Finite Group DatabasebetaFinite Group Databasebeta| order | 23940 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×D35×#4296 |
| unambiguous semidirect product | (C2×C5)⋊(D7×#4296) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D35×#4296 |
| commutator, hypocenter | C5×C7×C19 | C22×C9 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C7×C19 | C2×C9 |
| prime radical | C2×C19⋊C3×D35 | C3 |
| cosocle | C5×C7×C19⋊C3 | C22×C3 |
| LCS | G ▷ C5×C7×C19 | |
| UCS | C1 ◁ C2 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1330 |
418 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23940, 381);