Finite Group DatabasebetaFinite Group Databasebeta| order | 20100 |
| isoclinism | isoclinic class of A5 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C67 · Schur multiplier (H2) = C2 |
| direct product | C5×A5×C67 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C5×C67 | A5 |
| commutator, hypocenter | A5 | C5×C67 |
| Frattini | C1 | G |
| LCS | G ▷ A5 | |
| UCS | C1 ◁ C5×C67 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 1675 |
A minimal faithful permutation representation — 2 generators on 77 points:
(73,74)(75,77);(1,2,3,4,5)(6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72)(73,74,75,77,76)1675 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20100, 165);