Finite Group DatabasebetaFinite Group Databasebeta| order | 3968 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2032 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C31 · Schur multiplier (H2) = C23 |
| direct product | C31×#2032 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C31 | #393 |
| commutator, Frattini, cosocle | C24 | C23×C31 |
| prime radical | C22×D4×C31 | C22 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C31 ◁ C24×C31 ◁ G | |
278 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 80 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)(34,37)(35,42,44,38)(36,39)(40,47,43,45)(41,46);(32,34)(33,37)(35,43,44,40)(36,41)(38,45,42,47)(39,46);(32,35)(33,38)(34,40)(36,44)(37,45)(39,42)(41,43)(46,47)713 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C31×#2032, C31×#23474, C31×#23996, … |
| maximal normal subgroup of | C2×C31×#2032, C31×#23474, C31×#23996, … |
| maximal quotient of | C31×#10374, C31×#10375, C31×#10376, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3968, 764);