Finite Group DatabasebetaFinite Group Databasebeta| order | 19292 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C13 · Schur multiplier (H2) = C2 |
| direct product | C2×D7×C53⋊C13 |
| unambiguous semidirect product | C7⋊(C22×C53⋊C13) |
| unambiguous semidirect product | (C2×C7)⋊(C2×C53⋊C13) |
| unambiguous semidirect product | (C2×D7×C53)⋊C13 |
| Fitting, socle | C2×C7×C53 ⋊ C2×C13 |
| derived, Hall | C7×C53 ⋊ C22×C13 |
| Hall | C7×C53⋊C13 ⋊ C22 |
| Hall | C2×D7×C53 ⋊ C13 |
| Sylow | C53 ⋊ C2×C13×D7 |
| Sylow | C7 ⋊ C22×C53⋊C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D7×C53⋊C13 |
| commutator, cosocle, hypocenter | C7×C53 | C22×C13 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C53 | C2×C13 |
| LCS | G ▷ C7×C53 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 742 |
170 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19292, 19);