Finite Group DatabasebetaFinite Group Databasebeta| order | 26011 |
| automorphism | ? |
| homology | Abelianization (H1) = C19 · Schur multiplier (H2) = C37 |
| unambiguous semidirect product | C372⋊C19 |
| Fitting, socle, derived, Sylow | C372 ⋊ C19 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C372 | C19 |
| LCS | G ▷ C372 | |
| UCS | C1 | |
6 conjugacy classes of subgroups.
| transitive degree | μt(G) = 703 |
Polycyclic presentation:
19,37^2|b^a=b^4c^25,c^a=b^24c^3091 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26011, 2);