Finite Group DatabasebetaFinite Group Databasebeta| order | 3904 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #465 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C61 · Schur multiplier (H2) = C4 |
| direct product | C61×#488 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C23×C61 |
| prime radical | C2×D4×C61 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C42×C61 ◁ G | |
96 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1952 |
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)(72,80)(73,76)(74,84)(75,79)(77,82)(78,81)(83,85);(63,66)(67,69)(70,72,81,83,75,82,74,73)(71,76,84,77,79,85,78,80);(62,64,65,68)(63,67,66,69)(70,73,74,82,75,83,81,72)(71,77,78,76,79,80,84,85)1342 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3904, 169);