Finite Group DatabasebetaFinite Group Databasebeta| order | 3968 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3026 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C31 · Schur multiplier (H2) = C25×C4 |
| direct product | C31×#3027 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C31 | C2×#120 |
| commutator, Frattini, cosocle | C23 | C24×C31 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C31 ◁ C22×C4×C31 ◁ G | |
772 conjugacy classes of subgroups; only the 212 normal subgroups are shown.
This group has 772 conjugacy classes of subgroups — too many to draw. Only its 212 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 — 4 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)(35,42)(37,43)(38,45)(40,46);(32,33)(34,37)(35,38)(36,39)(40,44)(41,43)(42,45)(46,47);(32,34)(33,37)(35,40)(36,41)(38,44)(39,43)(42,46)(45,47);(32,35,36,42)(33,38,39,45)(34,40,41,46)(37,44,43,47)899 conjugacy classes — view the full character table.
| maximal subgroup of | C31×#13350, C31×#13351, C31×#13353, … |
| maximal normal subgroup of | C31×#13350, C31×#13351, C31×#13353, … |
| maximal quotient of | C31×#18300, C31×#18301, C31×#18302, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3968, 1759);