Finite Group DatabasebetaFinite Group Databasebeta| order | 3968 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1999 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C31 · Schur multiplier (H2) = C23 |
| direct product | C31×#2077 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C31 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C23×C31 |
| prime radical | C24×C31 | D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C31 ◁ C23×C4×C31 ◁ G | |
256 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 96 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 — 3 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)(38,41)(39,40)(42,43)(44,45,48,49,47,51,46,50);(32,33)(34,35)(37,40)(41,43);(33,35)(36,38,39,42)(37,41,40,43)(45,49)(46,48)(50,51)992 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C31×#2077, C31×#23638, C31×#23640, … |
| maximal normal subgroup of | C2×C31×#2077, C31×#23638, C31×#23640, … |
| maximal quotient of | C31×#10619, C31×#10620, C31×#10625, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3968, 809);