Finite Group DatabasebetaFinite Group Databasebeta| order | 14706 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C19×C43 ⋊ C2×C9 |
| Hall | #20301354 ⋊ C2 |
| Hall | D817 ⋊ C9 |
| Sylow | C43 ⋊ AGL(1,𝔽19) |
| Sylow | C19 ⋊ D43⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C19×C43 | C2×C9 |
| prime radical | (C19⋊C3)⋊D43 | C3 |
| cosocle | C43×C19⋊C3 | C2×C3 |
| LCS | G ▷ C19×C43 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 817 |
Polycyclic presentation:
2,3^2,19,43|b^3=c,d^a=d^18,e^a=e^42,d^b=d^4,e^b=e^6,d^c=d^782 conjugacy classes — view the full character table.
| maximal subgroup of | #28413672⋊C2, C2×#28413672 |
| maximal normal subgroup of | #28413672⋊C2, C2×#28413672 |
| maximal quotient of | #44440906, C2×#28413672 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14706, 28);