Finite Group DatabasebetaFinite Group Databasebeta| order | 1976 |
| isoclinism | isoclinic class of D19 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C23 |
| direct product | C22×C13×D19 |
| unambiguous semidirect product | C19⋊(C23×C13) |
| unambiguous semidirect product | (C2×C19)⋊(C22×C13) |
| Fitting, socle | C22×C13×C19 ⋊ C2 |
| derived, Sylow | C19 ⋊ C23×C13 |
| Hall | C13×C19 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C13 | D19 |
| commutator, cosocle, hypocenter | C19 | C23×C13 |
| Frattini | C1 | G |
| Fitting, socle | C22×C13×C19 | C2 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C22×C13 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 988 |
572 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1976, 36);