Finite Group DatabasebetaFinite Group Databasebeta| order | 3904 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C25 |
| direct product | C61×#578 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C61 | C22×D4 |
| commutator, Frattini, cosocle | C4 | C24×C61 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C61 ◁ #41×C61 ◁ G | |
248 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 1952 |
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)(62,63,67,71)(64,72,75,85)(65,69,76,83)(66,78,80,70)(68,79,82,74)(73,86,87,93)(77,90,89,84)(81,91,92,88);(62,64,67,75)(63,68,71,82)(65,73,76,87)(66,79,80,74)(69,81,83,92)(70,85,78,72)(77,91,89,88)(84,93,90,86);(62,65)(63,69)(64,73)(66,77)(67,76)(68,81)(70,84)(71,83)(72,86)(74,88)(75,87)(78,90)(79,91)(80,89)(82,92)(85,93);(65,76)(69,83)(73,87)(77,89)(81,92)(84,90)(86,93)(88,91)1342 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3904, 259);