Finite Group DatabasebetaFinite Group Databasebeta| order | 3968 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2184 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C31 · Schur multiplier (H2) = C2 |
| direct product | C31×#2229 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C31 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C23×C31 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C31 ◁ C42×C31 ◁ C4×C8×C31 ◁ G | |
124 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 71 |
| transitive degree | μt(G) = 3968 |
A minimal faithful permutation representation — 3 generators on 71 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)(32,33,35,37)(34,38,39,36)(40,41,43,46)(42,50,51,68)(44,56,54,69)(45,59,55,49)(47,63,61,52)(48,65,62,58)(53,70,60,66)(57,67,71,64);(32,34,35,39)(33,36,37,38)(41,46)(47,61)(48,62)(49,59)(50,68)(56,69)(64,67)(66,70);(40,42,43,51)(41,47,46,61)(44,57,54,71)(45,60,55,53)(48,66,62,70)(49,67,59,64)(50,69,68,56)(52,65,63,58)899 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C31×#2229, C31×#33626, C31×#33628, … |
| maximal normal subgroup of | C2×C31×#2229, C31×#33626, C31×#33628, … |
| maximal quotient of | C31×#12814, C31×#12936, C31×#12938, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3968, 961);