Finite Group DatabasebetaFinite Group Databasebeta| order | 19306 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C49 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #23751532⋊C2 |
| derived, Sylow | C197 ⋊ C2×C49 |
| Hall | #23751532 ⋊ C2 |
| Hall | D197 ⋊ C49 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C7 | D197⋊C7 |
| commutator, hypocenter | C197 | C2×C49 |
| Fitting, socle, cosocle | C7×C197 | C2×C7 |
| prime radical | C7×D197 | C7 |
| LCS | G ▷ C197 | |
| UCS | C1 ◁ C7 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,7,197,7|b^7=d,c^a=c^196,c^b=c^104196 conjugacy classes — view the full character table.
| maximal subgroup of | #50310999, C2×#23751532⋊C2 |
| maximal normal subgroup of | #50310999, C2×#23751532⋊C2 |
| maximal quotient of | #50310993, C2×#23751532⋊C2 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19306, 2);