Finite Group DatabasebetaFinite Group Databasebeta| order | 35226 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C19×C103 ⋊ C2×C9 |
| Hall | #31798584 ⋊ C2 |
| Hall | D1957 ⋊ C9 |
| Sylow | C103 ⋊ AGL(1,𝔽19) |
| Sylow | C19 ⋊ D103⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C19×C103 | C2×C9 |
| prime radical | (C19⋊C3)⋊D103 | C3 |
| cosocle | C19⋊C3×C103 | C2×C3 |
| LCS | G ▷ C19×C103 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1957 |
Polycyclic presentation:
2,3^2,19,103|b^3=c,d^a=d^18,e^a=e^102,d^b=d^4,e^b=e^56,d^c=d^7172 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35226, 28);