Finite Group DatabasebetaFinite Group Databasebeta| order | 3904 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C61 · Schur multiplier (H2) = C22×C4 |
| direct product | C61×#410 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C61 | C22⋊C4 |
| commutator | C22 | C22×C4×C61 |
| Frattini, cosocle | C23 | C23×C61 |
| socle | C2×C61 | C2×C22⋊C4 |
| prime radical | C2×#41×C61 | C2 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C61 ◁ C22×C4×C61 ◁ G | |
158 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 976 |
A minimal faithful permutation representation — 3 generators on 77 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)(64,70,72,67)(65,68)(66,69)(71,76,77,74)(73,75);(62,64)(63,67)(65,71)(66,72)(68,74)(69,70)(73,77)(75,76);(62,65,66,73)(63,68,69,75)(64,71,72,77)(67,74,70,76)1342 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3904, 91);