Finite Group DatabasebetaFinite Group Databasebeta| order | 3904 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of AΣL(1,𝔽16) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C61 · Schur multiplier (H2) = C22 |
| direct product | C61×AΣL(1,𝔽16) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C61 | #99 |
| commutator | C23 | C2×C4×C61 |
| Frattini, cosocle | C2×D4 | C22×C61 |
| prime radical | #120×C61 | C2 |
| LCS | G ▷ C23 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C61 ◁ C22×C61 ◁ C2×D4×C61 ◁ G | |
94 conjugacy classes of subgroups.
| minimal degree | μ(G) = 69 |
| transitive degree | μt(G) = 488 |
A minimal faithful permutation representation — 2 generators on 69 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)(64,68,69,66)(65,67);(63,66)(67,68)793 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3904, 32);