Finite Group DatabasebetaFinite Group Databasebeta| order | 3904 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #560 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C24 |
| direct product | C61×#564 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C61 | C24 |
| commutator, Frattini, cosocle | C22 | C24×C61 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ G | |
172 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 3904 |
A minimal faithful permutation representation — 4 generators on 93 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)(64,70)(65,73)(67,71)(68,75)(78,79,82,85)(80,83,88,86)(81,89,90,84)(87,92,93,91);(62,63,66,69)(64,71,70,67)(65,68,73,75)(72,77,76,74)(78,79)(80,86)(81,89)(82,85)(83,88)(84,90)(87,91)(92,93);(62,64,66,70)(63,67,69,71)(65,72,73,76)(68,74,75,77)(78,80)(79,83)(81,87)(82,88)(84,91)(85,86)(89,92)(90,93);(62,65)(63,68)(64,72)(66,73)(67,74)(69,75)(70,76)(71,77)(78,81,82,90)(79,84,85,89)(80,87,88,93)(83,91,86,92)1159 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3904, 245);