Finite Group DatabasebetaFinite Group Databasebeta| order | 3968 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2021 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C31 · Schur multiplier (H2) = C24 |
| direct product | C31×#2029 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C31 | #120 |
| commutator, Frattini, cosocle | C24 | C23×C31 |
| prime radical | C25×C31 | C22 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C31 ◁ C24×C31 ◁ G | |
466 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 496 |
A minimal faithful permutation representation — 3 generators on 47 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)(32,33,35,38)(34,40,41,37)(36,39,43,45)(42,46,47,44);(32,34,35,41)(33,37,38,40)(36,42,43,47)(39,44,45,46);(37,44)(40,46)806 conjugacy classes — view the full character table.
| maximal subgroup of | C31×#7426, C31×#12202, C31×#12203, … |
| maximal normal subgroup of | C31×#7426, C31×#12202, C31×#12203, … |
| maximal quotient of | C31×#10340, C31×#10341, C31×#10344, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3968, 761);