Finite Group DatabasebetaFinite Group Databasebeta| order | 1950 |
| isoclinism | isoclinic class of C13⋊C3×C5⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C5 |
| direct product | C13⋊C3×C5⋊D5 |
| unambiguous semidirect product | C5⋊(D5×C13⋊C3) |
| Fitting, socle, derived, Hall | C52×C13 ⋊ C2×C3 |
| Hall | C52×C13⋊C3 ⋊ C2 |
| Hall | C13×C5⋊D5 ⋊ C3 |
| Sylow | C52 ⋊ C2×C13⋊C3 |
| Sylow | C13 ⋊ C3×C5⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C13 | C2×C3 |
| LCS | G ▷ C52×C13 | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 325 |
A minimal faithful permutation representation — 3 generators on 23 points:
(2,3,5)(4,7,10)(6,9,8)(11,13,12)(15,16)(17,18)(20,21)(22,23);(1,2,4,3,6,10,7,11,13,5,8,12,9)(19,20,22,23,21);(14,15,17,18,16)98 conjugacy classes — view the full character table.
| maximal subgroup of | #16839083, C13⋊C3×#1043, #13049932⋊C3, … |
| maximal normal subgroup of | #16839083, C13⋊C3×#1043, #13049932⋊C3, … |
| maximal quotient of | C13⋊C3×#1039, C2×C13⋊C3×C5⋊D5, C7×C13⋊C3×C5⋊D5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1950, 18);