Finite Group DatabasebetaFinite Group Databasebeta| order | 3904 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of B(4,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C61 · Schur multiplier (H2) = C23 |
| direct product | C61×#458 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C61 | #120 |
| commutator, Frattini, cosocle | C23 | C23×C61 |
| prime radical | H(5,𝔽2)×C61 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C61 ◁ C23×C61 ◁ G | |
160 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 976 |
A minimal faithful permutation representation — 3 generators on 77 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)(62,63,66,69)(64,67,71,74)(65,68,72,75)(70,76,77,73);(62,64)(63,67)(65,70)(66,71)(68,73)(69,74)(72,77)(75,76);(62,65)(63,68)(64,70)(66,72)(67,73)(69,75)(71,77)(74,76)976 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3904, 139);