Finite Group DatabasebetaFinite Group Databasebeta| order | 18772 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C19 · Schur multiplier (H2) = C2 |
| direct product | C2×C19×D247 |
| unambiguous semidirect product | (C2×C13)⋊(C19×D19) |
| unambiguous semidirect product | (C2×C19)⋊(C19×D13) |
| Fitting, socle | C2×C13×C192 ⋊ C2 |
| derived | C13×C19 ⋊ C22×C19 |
| Hall | C13×C192 ⋊ C22 |
| Sylow | C192 ⋊ C2×D13 |
| Sylow | C13 ⋊ C2×C19×D19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C19 | D247 |
| commutator, cosocle, hypocenter | C13×C19 | C22×C19 |
| Frattini | C1 | G |
| Fitting, socle | C2×C13×C192 | C2 |
| LCS | G ▷ C13×C19 | |
| UCS | C1 ◁ C2×C19 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 988 |
4750 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18772, 31);