Finite Group DatabasebetaFinite Group Databasebeta| order | 18772 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C13 · Schur multiplier (H2) = C2 |
| direct product | C13×D192 |
| unambiguous semidirect product | (C19×D19)⋊(C2×C13) |
| unambiguous semidirect product | (C19⋊D19)⋊(C2×C13) |
| Fitting, socle, Hall | C13×C192 ⋊ C22 |
| derived, Sylow | C192 ⋊ C22×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | D192 |
| commutator, cosocle, hypocenter | C192 | C22×C13 |
| Frattini | C1 | G |
| Fitting, socle | C13×C192 | C22 |
| LCS | G ▷ C192 | |
| UCS | C1 ◁ C13 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 494 |
1573 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18772, 19);