Finite Group DatabasebetaFinite Group Databasebeta| order | 19306 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C72 · Schur multiplier (H2) = C7 |
| direct product | C7×D197⋊C7 |
| unambiguous semidirect product | D197⋊C72 |
| unambiguous semidirect product | (C197⋊C7)⋊(C2×C7) |
| unambiguous semidirect product | (C7×D197)⋊C7 |
| Fitting, socle | C7×C197 ⋊ C2×C7 |
| derived, Sylow | C197 ⋊ C2×C72 |
| Hall | C7×C197⋊C7 ⋊ C2 |
| Hall | D197 ⋊ C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D197⋊C7 |
| commutator, cosocle, hypocenter | C197 | C2×C72 |
| Frattini | C1 | G |
| Fitting, socle | C7×C197 | C2×C7 |
| LCS | G ▷ C197 | |
| UCS | C1 ◁ C7 | |
40 conjugacy classes of subgroups.
196 conjugacy classes — view the full character table.
| maximal subgroup of | C7×#11716161⋊C7, C7⋊(#11716161⋊C7), D7×D197⋊C7, … |
| maximal normal subgroup of | C7×#11716161⋊C7, C7⋊(#11716161⋊C7), D7×D197⋊C7, … |
| maximal quotient of | C7×Dic197⋊C7, C2×C7×D197⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19306, 10);