Finite Group DatabasebetaFinite Group Databasebeta| order | 3904 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #509 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C61 · Schur multiplier (H2) = C22 |
| direct product | C61×#510 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C61 | C2×D8 |
| commutator, Frattini, cosocle | C8 | C23×C61 |
| prime radical | #135×C61 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C61 ◁ C2×C4×C61 ◁ C2×C8×C61 ◁ G | |
82 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)(64,72)(65,76)(66,81)(67,69)(68,73)(70,79)(71,78)(74,92)(75,89)(77,87)(80,88)(82,86)(83,91)(84,93)(85,90);(62,64,67,75)(63,68,69,83)(65,77,80,93)(66,82,78,74)(70,86,85,92)(71,87,81,84)(72,88,89,76)(73,90,91,79);(63,69)(68,83)(70,85)(71,81)(72,89)(76,88)(84,87)(86,92)976 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3904, 191);