Finite Group DatabasebetaFinite Group Databasebeta| order | 3968 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1619 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C31 · Schur multiplier (H2) = C22 |
| direct product | C31×#1628 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C31 | #120 |
| commutator, Frattini, cosocle | C42 | C23×C31 |
| prime radical | C31×#459 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C31 ◁ C42×C31 ◁ G | |
216 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 68 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) = 1984 |
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)(33,37)(34,35)(38,39)(41,42)(43,44)(46,47);(32,33)(34,37)(35,39)(36,38)(40,41,45,47)(42,43,46,44);(32,34,36,35)(33,37,38,39)(40,42)(41,43)(44,47)(45,46)806 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C31×#1628, C31×#18494, C31×#18520, … |
| maximal normal subgroup of | C2×C31×#1628, C31×#18494, C31×#18520, … |
| maximal quotient of | C31×#7740, C31×#7744, C31×#7746, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3968, 360);