Finite Group DatabasebetaFinite Group Databasebeta| order | 13260 |
| isoclinism | isoclinic class of C3⋊#261 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C17 · Schur multiplier (H2) = C1 |
| direct product | C5×C17×C3⋊#261 |
| unambiguous semidirect product | C3⋊(C5×C17×#261) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C17 | C3⋊#261 |
| commutator, hypocenter | C3×C13 | C4×C5×C17 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C13×C17 | C4 |
| prime radical | C3×C5×C17×D13 | C2 |
| cosocle | C3×D13 | C2×C5×C17 |
| LCS | G ▷ C3×C13 | |
| UCS | C1 ◁ C5×C17 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 38 |
| transitive degree | μt(G) = 3315 |
A minimal faithful permutation representation — 2 generators on 38 points:
(2,3,4,6)(5,8,9,10)(7,12,13,11)(15,16)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33)(34,35,36,37,38);(1,2,5,10,12,3,7,13,6,11,8,9,4)(14,15,16)1275 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13260, 105);