Finite Group DatabasebetaFinite Group Databasebeta| order | 2382 |
| isoclinism | isoclinic class of D397 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D397 |
| Fitting, socle, Hall | C3×C397 ⋊ C2 |
| derived, Sylow | C397 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D397 |
| commutator, cosocle, hypocenter | C397 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C397 | C2 |
| LCS | G ▷ C397 | |
| UCS | C1 ◁ C3 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 400 |
| transitive degree | μt(G) = 1191 |
600 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#13097544, C3⋊#13097544, D3×D397, … |
| maximal normal subgroup of | C3×#13097544, C3⋊#13097544, D3×D397, … |
| maximal quotient of | C3×Dic397, C2×C3×D397, C3×C5×D397, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2382, 4);