Finite Group DatabasebetaFinite Group Databasebeta| order | 2316 |
| isoclinism | isoclinic class of D3×D193 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D3×D193 |
| unambiguous semidirect product | (D3×C193)⋊C2 |
| unambiguous semidirect product | (C3×D193)⋊C2 |
| unambiguous semidirect product | D579⋊C2 |
| Fitting, socle, derived, Hall | C3×C193 ⋊ C22 |
| Sylow | C193 ⋊ C2×D3 |
| Sylow | C3 ⋊ C2×D193 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C193 | C22 |
| LCS | G ▷ C3×C193 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| minimal degree | μ(G) = 196 |
| transitive degree | μt(G) = 579 |
294 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D3×D193, D15×D193, D3×D965, … |
| maximal normal subgroup of | C5×D3×D193, D3×C7×D193, D3×C11×D193, … |
| maximal quotient of | C5×D3×D193, D15×D193, D3×D965, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2316, 12);