Finite Group DatabasebetaFinite Group Databasebeta| order | 3968 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2613 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C31 · Schur multiplier (H2) = C24 |
| direct product | C31×#2659 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C31 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C31 |
| prime radical | C24×C31 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C31 ◁ G | |
524 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 232 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 — 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)(38,40)(39,41)(42,43)(44,45,48,50)(46,47,51,49);(32,33,34,35)(36,37,39,41)(38,40,43,42)(44,46)(45,49)(47,50)(48,51);(32,33)(34,35)(36,37)(38,42)(39,41)(40,43)(44,47,48,49)(45,46,50,51);(36,38)(37,40)(39,43)(41,42)(44,46)(45,47)(48,51)(49,50)992 conjugacy classes — view the full character table.
| maximal subgroup of | C31×#9966, C31×#9967, C31×#9972, … |
| maximal normal subgroup of | C31×#9966, C31×#9967, C31×#9972, … |
| maximal quotient of | C31×#14275, C31×#14281, C31×#14327, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3968, 1391);