Finite Group DatabasebetaFinite Group Databasebeta| order | 3904 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #471 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C61 · Schur multiplier (H2) = C22 |
| direct product | C61×#473 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C61 | #121 |
| commutator, Frattini, cosocle | C2×C4 | C23×C61 |
| prime radical | #41×C61 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C61 ◁ C2×C4×C61 ◁ G | |
100 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 1952 |
A minimal faithful permutation representation — 3 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)(62,63,68,73)(64,74,78,84)(65,79,81,87)(66,72,67,71)(69,77,85,76)(70,82,86,80)(75,89,91,83)(88,92,93,90);(62,64,67,77,68,78,66,76)(63,69,72,84,73,85,71,74)(65,75,82,92,81,91,80,90)(70,83,87,93,86,89,79,88);(62,65)(63,70)(64,75)(66,80)(67,82)(68,81)(69,83)(71,79)(72,87)(73,86)(74,88)(76,90)(77,92)(78,91)(84,93)(85,89)976 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3904, 154);