Finite Group DatabasebetaFinite Group Databasebeta| order | 19306 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C49 · Schur multiplier (H2) = C1 |
| direct product | C2×#23751532 |
| derived, Sylow | C197 ⋊ C2×C49 |
| Hall | C2×C197 ⋊ C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | C197⋊C7 |
| commutator, hypocenter | C197 | C2×C49 |
| Frattini | C7 | C2×C197⋊C7 |
| Fitting, socle, prime radical | C2×C7×C197 | C7 |
| cosocle | C7×C197 | C2×C7 |
| LCS | G ▷ C197 | |
| UCS | C1 ◁ C2×C7 | |
12 conjugacy classes of subgroups.
490 conjugacy classes — view the full character table.
| maximal subgroup of | #50310993, C4×#23751532, C2×#23751532⋊C2, … |
| maximal normal subgroup of | #50310993, C4×#23751532, C2×#23751532⋊C2, … |
| maximal quotient of | C4×#23751532, C22×#23751532 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19306, 3);