Finite Group DatabasebetaFinite Group Databasebeta| order | 3968 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C31 · Schur multiplier (H2) = C24 |
| direct product | C31×#2399 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C31 | C23 |
| commutator, Frattini, cosocle | C23 | C24×C31 |
| socle, prime radical | C23×C31 | C24 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C31 ◁ G | |
504 conjugacy classes of subgroups; only the 248 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 248 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) = 3968 |
A minimal faithful permutation representation — 4 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)(36,37,40,43)(38,42,39,41)(44,45,48,51)(46,50,47,49);(32,33)(34,35)(36,38,40,39)(37,41,43,42)(44,46,48,47)(45,49,51,50);(33,35)(36,38,40,39)(37,42,43,41)(44,47,48,46)(45,50,51,49);(36,39,40,38)(37,41,43,42)1364 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C31×#9030, C31×#10014, C31×#10017, … |
| maximal normal subgroup of | C31×#9030, C31×#10014, C31×#10017, … |
| maximal quotient of | C31×#13848, C31×#13850, C31×#13856, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3968, 1131);