Finite Group DatabasebetaFinite Group Databasebeta| order | 38220 |
| automorphism | ? |
| homology | Abelianization (H1) = C13×C49 · Schur multiplier (H2) = C2 |
| direct product | C13×C49×A5 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C13×C49 | A5 |
| commutator, hypocenter | A5 | C13×C49 |
| Frattini, cosocle | C7 | C7×C13×A5 |
| socle, prime radical | C7×C13×A5 | C7 |
| LCS | G ▷ A5 | |
| UCS | C1 ◁ C13×C49 | |
54 conjugacy classes of subgroups.
| minimal degree | μ(G) = 67 |
| transitive degree | μt(G) = 3185 |
A minimal faithful permutation representation — 2 generators on 67 points:
(1,4,2,3,5);(1,2,3,4,5)(6,7,8,9,10,11,12,13,14,15,16,17,18)(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67)3185 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38220, 1219);