Finite Group DatabasebetaFinite Group Databasebeta| order | 1950 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52×C13 · Schur multiplier (H2) = C5 |
| direct product | C52×D3×C13 |
| unambiguous semidirect product | C3⋊(C2×C52×C13) |
| Fitting, socle, Hall | C3×C52×C13 ⋊ C2 |
| derived, Sylow | C3 ⋊ C2×C52×C13 |
| Hall | C3×C52 ⋊ C2×C13 |
| Hall | C3×C13 ⋊ C2×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52×C13 | D3 |
| commutator, cosocle, hypocenter | C3 | C2×C52×C13 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C13 | C2 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C52×C13 | |
64 conjugacy classes of subgroups.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 975 |
A minimal faithful permutation representation — 2 generators on 26 points:
(1,2,3,4,5)(11,12,13)(14,15,16,17,18,19,20,21,22,23,24,25,26);(6,7,8,9,10)(12,13)975 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C52×D3×D13, C5×D3×D5×C13, C5×D3×D65, … |
| maximal normal subgroup of | C52×D3×D13, C5×D3×D5×C13, C5×D3×D65, … |
| maximal quotient of | C52×Dic3×C13, C2×C52×D3×C13, C52×C13×D21, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1950, 34);