Finite Group DatabasebetaFinite Group Databasebeta| order | 26220 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×Dic1311 |
| unambiguous semidirect product | C3⋊(C5×Dic437) |
| unambiguous semidirect product | C19⋊(C5×Dic69) |
| unambiguous semidirect product | C23⋊(C5×Dic57) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D1311 |
| commutator, hypocenter | C3×C19×C23 | C4×C5 |
| Frattini | C2 | C5×D1311 |
| Fitting, socle, prime radical | C2×C3×C5×C19×C23 | C2 |
| cosocle | C2×C3×C19×C23 | C2×C5 |
| LCS | G ▷ C3×C19×C23 | |
| UCS | C1 ◁ C2×C5 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 26220 |
6570 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26220, 13);