Finite Group DatabasebetaFinite Group Databasebeta| order | 1026 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C9×C19 ⋊ C2×C3 |
| Hall | #10587023 ⋊ C2 |
| Hall | D19 ⋊ 3−1+2 |
| Sylow | C19 ⋊ C2×3−1+2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C3×D19⋊C3 |
| commutator, socle, cosocle | C3×C19 | C2×C32 |
| Fitting | C9×C19 | C2×C3 |
| prime radical | C3×D19⋊C3 | C3 |
| hypercenter | C9 | D19⋊C3 |
| hypocenter | C19 | C2×3−1+2 |
| LCS | G ▷ C3×C19 ▷ C19 | |
| UCS | C1 ◁ C3 ◁ C9 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 171 |
Polycyclic presentation:
2,3^3,19|c^3=d,e^a=e^18,c^b=cd,e^b=e^1149 conjugacy classes — view the full character table.
| maximal subgroup of | 3−1+2×D19⋊C3, #72244848 |
| maximal normal subgroup of | 3−1+2×D19⋊C3, #72244848 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1026, 10);