Finite Group DatabasebetaFinite Group Databasebeta| order | 19306 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C49 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #23751534⋊C2 |
| Fitting, socle, derived, Sylow | C197 ⋊ C2×C49 |
| Hall | #23751534 ⋊ C2 |
| Hall | D197 ⋊ C49 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C197 | C2×C49 |
| prime radical | D197⋊C7 | C7 |
| cosocle | C197⋊C7 | C2×C7 |
| LCS | G ▷ C197 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,7^2,197|b^7=c,d^a=d^196,d^b=d^16,d^c=d^104100 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽197), C2×#23751534⋊C2 |
| maximal normal subgroup of | AGL(1,𝔽197), C2×#23751534⋊C2 |
| maximal quotient of | #50311009, C2×#23751534⋊C2 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19306, 8);