Finite Group DatabasebetaFinite Group Databasebeta| order | 1950 |
| isoclinism | isoclinic class of C13⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C52 · Schur multiplier (H2) = C5 |
| direct product | C2×C52×C13⋊C3 |
| unambiguous semidirect product | (C2×C13)⋊(C3×C52) |
| unambiguous semidirect product | (C2×C5×C13)⋊(C3×C5) |
| Fitting, socle, Hall | C2×C52×C13 ⋊ C3 |
| derived, Sylow | C13 ⋊ C2×C3×C52 |
| Hall | C52×C13 ⋊ C2×C3 |
| Hall | C2×C13 ⋊ C3×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C52 | C13⋊C3 |
| commutator, cosocle, hypocenter | C13 | C2×C3×C52 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52×C13 | C3 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C2×C52 | |
64 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 650 |
A minimal faithful permutation representation — 2 generators on 25 points:
(1,2)(3,4,5,6,7)(14,15,17)(16,19,22)(18,21,20)(23,25,24);(8,9,10,11,12)(13,14,16,15,18,22,19,23,25,17,20,24,21)350 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C52×Dic13⋊C3, C5×Dic5×C13⋊C3, C5×Dic65⋊C3, … |
| maximal normal subgroup of | C52×Dic13⋊C3, C5×Dic5×C13⋊C3, C5×Dic65⋊C3, … |
| maximal quotient of | C4×C52×C13⋊C3, C22×C52×C13⋊C3, C52×#10587720, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1950, 26);