Finite Group DatabasebetaFinite Group Databasebeta| order | 3904 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C61 · Schur multiplier (H2) = C2 |
| direct product | C61×Q8⋊C8 |
| unambiguous semidirect product | Q8⋊(C8×C61) |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C61 | D4 |
| commutator | C4 | C2×C8×C61 |
| Frattini, cosocle | C42 | C22×C61 |
| socle, prime radical | C22×C61 | C22⋊C4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C61 ◁ C42×C61 ◁ G | |
70 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 3904 |
A minimal faithful permutation representation — 2 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)(63,66)(64,68)(67,69)(70,71,72,74,73,75,76,77);(62,63,65,67)(64,69,68,66)1708 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3904, 7);