Finite Group DatabasebetaFinite Group Databasebeta| order | 3968 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3026 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C31 · Schur multiplier (H2) = C26 |
| direct product | C31×#3028 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C31 | C2×#120 |
| commutator, Frattini, cosocle | C23 | C24×C31 |
| prime radical | C31×#585 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C31 ◁ C22×C4×C31 ◁ G | |
716 conjugacy classes of subgroups; only the 212 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 212 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 63 |
| transitive degree | μt(G) = 992 |
A minimal faithful permutation representation — 4 generators on 63 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)(32,33,37,41)(34,38,44,51)(35,39,46,53)(36,47,48,40)(42,54,56,49)(43,57,58,50)(45,59,60,52)(55,61,63,62);(32,34)(33,38)(35,42)(36,43)(37,44)(39,49)(40,50)(41,51)(45,55)(46,56)(47,57)(48,58)(52,61)(53,54)(59,62)(60,63);(32,35)(33,39)(34,42)(36,45)(37,46)(38,49)(40,52)(41,53)(43,55)(44,56)(47,59)(48,60)(50,61)(51,54)(57,62)(58,63);(32,36,37,48)(33,40,41,47)(34,43,44,58)(35,45,46,60)(38,50,51,57)(39,52,53,59)(42,55,56,63)(49,61,54,62)899 conjugacy classes — view the full character table.
| maximal subgroup of | C31×#13351, C31×#13352, C31×#13354, … |
| maximal normal subgroup of | C31×#13351, C31×#13352, C31×#13354, … |
| maximal quotient of | C31×#18308, C31×#18309, C31×#18310, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3968, 1760);