Finite Group DatabasebetaFinite Group Databasebeta| order | 3968 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2018 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C31 · Schur multiplier (H2) = C22 |
| direct product | C31×#2064 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C31 | #121 |
| commutator, Frattini, cosocle | C22×C4 | C23×C31 |
| prime radical | C23×C31 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C31 ◁ C22×C4×C31 ◁ G | |
208 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 208 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) = 51 |
| transitive degree | μt(G) = 1984 |
A minimal faithful permutation representation — 3 generators on 51 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)(36,37,40,47,42,46,41,45)(38,44,48,43,39,50,49,51);(32,33)(34,35)(36,38,40,48,42,39,41,49)(37,43,45,44,46,51,47,50);(33,35)(36,39,42,38)(37,44,46,50)(40,48,41,49)(43,47,51,45)806 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C31×#2064, C31×#23601, C31×#23603, … |
| maximal normal subgroup of | C2×C31×#2064, C31×#23601, C31×#23603, … |
| maximal quotient of | C31×#10588, C31×#10590, C31×#10592, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3968, 796);