Finite Group DatabasebetaFinite Group Databasebeta| order | 3904 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C61 · Schur multiplier (H2) = C22 |
| direct product | C61×#400 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C61 | C23 |
| commutator, Frattini, cosocle | C23 | C23×C61 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C61 ◁ G | |
134 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)(68,72)(70,73)(74,75,77,79)(76,80,81,78);(63,65)(66,67,69,71)(68,73,72,70)(74,75)(76,80)(77,79)(78,81);(62,63)(64,65)(66,68)(67,70)(69,72)(71,73)(74,76,77,81)(75,78,79,80)1342 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3904, 81);