Finite Group DatabasebetaFinite Group Databasebeta| order | 1976 |
| isoclinism | isoclinic class of D19×#261 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | D19×#261 |
| unambiguous semidirect product | (C19×#261)⋊C2 |
| unambiguous semidirect product | (C19⋊#261)⋊C2 |
| Fitting, socle, derived, Hall | C13×C19 ⋊ C2×C4 |
| Sylow | C19 ⋊ C2×#261 |
| Sylow | C13 ⋊ C4×D19 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C19 | C2×C4 |
| prime radical | D13×D19 | C2 |
| cosocle | C19×D13 | C22 |
| LCS | G ▷ C13×C19 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 247 |
77 conjugacy classes — view the full character table.
| maximal subgroup of | #261×D19⋊C3, D19×AGL(1,𝔽13), #72277826, … |
| maximal normal subgroup of | #261×D19⋊C3, D19×AGL(1,𝔽13), #72277826, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1976, 32);