Finite Group DatabasebetaFinite Group Databasebeta| order | 3904 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #468 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C61 · Schur multiplier (H2) = C4 |
| direct product | C61×#491 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C61 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C23×C61 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C42×C61 ◁ G | |
90 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 3904 |
A minimal faithful permutation representation — 3 generators on 85 points:
(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)(64,67)(65,66)(68,69)(70,71,76,81)(72,78,83,84)(73,77,82,85)(74,80,75,79);(63,66)(67,69)(70,72,74,73,76,83,75,82)(71,77,79,78,81,85,80,84);(62,64,65,68)(63,67,66,69)(70,73,74,83,76,82,75,72)(71,78,79,85,81,84,80,77)976 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3904, 172);