Finite Group DatabasebetaFinite Group Databasebeta| order | 26524 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C19⋊#13063703 |
| Fitting, socle, derived, Hall | C19×C349 ⋊ C4 |
| Sylow | C349 ⋊ Dic19 |
| Sylow | C19 ⋊ #13063703 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C19×C349 | C4 |
| prime radical, cosocle | C19×D349 | C2 |
| LCS | G ▷ C19×C349 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6631 |
Polycyclic presentation:
2^2,19,349|a^2=b,c^a=c^18,d^a=d^136,d^b=d^3481675 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26524, 7);