Finite Group DatabasebetaFinite Group Databasebeta| order | 3904 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #534 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C24 |
| direct product | C61×#541 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | C24 |
| commutator, Frattini, cosocle | C22 | C24×C61 |
| prime radical | C23×C61 | C23 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ G | |
192 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1952 |
A minimal faithful permutation representation — 4 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)(64,68)(66,69)(70,71,74,77)(72,75,80,78)(73,81,82,76)(79,84,85,83);(62,63,65,67)(64,66,68,69)(70,71)(72,78)(73,76)(74,77)(75,80)(79,84)(81,82)(83,85);(62,64)(63,66)(65,68)(67,69)(70,72)(71,75)(73,79)(74,80)(76,83)(77,78)(81,84)(82,85);(70,73,74,82)(71,76,77,81)(72,79,80,85)(75,83,78,84)1342 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3904, 222);