Finite Group DatabasebetaFinite Group Databasebeta| order | 26210 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D2621⋊C5 |
| unambiguous semidirect product | (C2621⋊C5)⋊C2 |
| Fitting, socle, derived, Sylow | C2621 ⋊ C2×C5 |
| Hall | C2621⋊C5 ⋊ C2 |
| Hall | D2621 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C2621 | C2×C5 |
| LCS | G ▷ C2621 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2621 |
Polycyclic presentation:
2,5,2621|c^a=c^2620,c^b=c^1860272 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26210, 1);