Finite Group DatabasebetaFinite Group Databasebeta| order | 19698 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C49⋊C3)⋊D67 |
| Fitting, derived, Hall | C49×C67 ⋊ C2×C3 |
| Hall | C67×C49⋊C3 ⋊ C2 |
| Hall | D3283 ⋊ C3 |
| Hall | C49⋊C3 ⋊ D67 |
| Sylow | C67 ⋊ D49⋊C3 |
| Sylow | C49 ⋊ C3×D67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C49×C67 | C2×C3 |
| Frattini | C7 | ΓL(1,𝔽8)⋊D67 |
| socle | C7×C67 | AGL(1,𝔽7) |
| LCS | G ▷ C49×C67 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3283 |
Polycyclic presentation:
2,3,7,67,7|c^7=e^6,c^a=c^6e,d^a=d^66,e^a=e^6,c^b=c^2e^3,e^b=e^2641 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19698, 22);