Finite Group DatabasebetaFinite Group Databasebeta| order | 13020 |
| isoclinism | isoclinic class of A5 |
| automorphism | ? |
| homology | Abelianization (H1) = C7×C31 · Schur multiplier (H2) = C2 |
| direct product | C7×C31×A5 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C7×C31 | A5 |
| commutator, hypocenter | A5 | C7×C31 |
| Frattini | C1 | G |
| LCS | G ▷ A5 | |
| UCS | C1 ◁ C7×C31 | |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1085 |
A minimal faithful permutation representation — 2 generators on 43 points:
(40,42)(41,43);(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)(39,43,42)1085 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13020, 253);