Finite Group DatabasebetaFinite Group Databasebeta| order | 3904 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C61 · Schur multiplier (H2) = C23 |
| direct product | C61×#383 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C61 | C23 |
| commutator | C22 | C22×C4×C61 |
| Frattini, cosocle | C23 | C23×C61 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C61 ◁ G | |
138 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 3904 |
A minimal faithful permutation representation — 3 generators on 81 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)(62,63,64,65)(68,72)(70,73)(75,78)(76,80);(66,67,69,71)(68,70,72,73)(74,75)(76,79)(77,78)(80,81);(66,68)(67,70)(69,72)(71,73)(74,76,77,80)(75,79,78,81)1708 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3904, 64);