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×#551 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | C24 |
| commutator, Frattini, cosocle | C22 | C24×C61 |
| prime radical | #120×C61 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ G | |
248 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 150 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) = 976 |
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)(62,63,65,69)(64,70,71,67)(66,68,73,75)(72,76,77,74);(62,64,66,72)(63,67,68,74)(65,71,73,77)(69,70,75,76);(63,68)(67,74)(69,75)(70,76);(64,71)(67,70)(72,77)(74,76)1525 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3904, 232);