Finite Group DatabasebetaFinite Group Databasebeta| order | 3904 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #360 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C61 · Schur multiplier (H2) = C2 |
| direct product | C61×#360 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C61 | #102 |
| commutator | C8 | C2×C4×C61 |
| Frattini, cosocle | C2×C8 | C22×C61 |
| prime radical | #135×C61 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C61 ◁ C2×C4×C61 ◁ C2×C8×C61 ◁ G | |
58 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 976 |
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)(63,67,68,76)(64,70)(65,73)(69,71,74,77)(72,75);(62,63)(64,71)(65,74)(66,68)(67,75)(69,73)(70,76)(72,77)976 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3904, 41);