Finite Group DatabasebetaFinite Group Databasebeta| order | 3904 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D42 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C24 |
| direct product | C61×#554 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | C24 |
| commutator, Frattini, cosocle | C22 | C24×C61 |
| prime radical | C2×D4×C61 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ G | |
228 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 166 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 1952 |
A minimal faithful permutation representation — 4 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)(62,63,66,65)(64,68,69,67)(70,71,74,73)(72,76,77,75);(63,65)(67,68)(70,72,74,77)(71,75,73,76);(62,64)(63,67)(65,68)(66,69);(62,65,66,63)(64,68,69,67)(70,73,74,71)(72,75,77,76)1525 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3904, 235);