Finite Group DatabasebetaFinite Group Databasebeta| order | 1196 |
| isoclinism | isoclinic class of D13×D23 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D13×D23 |
| unambiguous semidirect product | (C23×D13)⋊C2 |
| unambiguous semidirect product | (C13×D23)⋊C2 |
| unambiguous semidirect product | D299⋊C2 |
| Fitting, socle, derived, Hall | C13×C23 ⋊ C22 |
| Sylow | C23 ⋊ C2×D13 |
| Sylow | C13 ⋊ C2×D23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C23 | C22 |
| LCS | G ▷ C13×C23 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 299 |
104 conjugacy classes — view the full character table.
| maximal subgroup of | D23×D13⋊C3, C3×D13×D23, D23×D39, … |
| maximal normal subgroup of | D23×D13⋊C3, C3×D13×D23, D13×AGL(1,𝔽23), … |
| maximal quotient of | C3×D13×D23, D23×D39, D13×D69, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1196, 7);