Finite Group DatabasebetaFinite Group Databasebeta| order | 3968 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2613 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C31 · Schur multiplier (H2) = C23×C4 |
| direct product | C31×#2660 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C31 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C31 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C31 ◁ G | |
448 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 448 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) = 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)(38,40)(39,41)(42,43)(44,45,48,46)(47,50,51,49);(32,33,34,35)(36,37,39,41)(38,40,43,42)(44,46,48,45)(47,49,51,50);(32,33)(34,35)(36,37)(38,42)(39,41)(40,43)(44,47,48,51)(45,49,46,50);(36,38,39,43)(37,40,41,42)992 conjugacy classes — view the full character table.
| maximal subgroup of | C31×#10091, C31×#10093, C31×#10099, … |
| maximal normal subgroup of | C31×#10091, C31×#10093, C31×#10099, … |
| maximal quotient of | C31×#14276, C31×#14277, C31×#14282, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3968, 1392);