Finite Group DatabasebetaFinite Group Databasebeta| order | 3968 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3019 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C31 · Schur multiplier (H2) = C26 |
| direct product | C31×#3022 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C31 | C2×#120 |
| commutator, Frattini, cosocle | C2×C4 | C24×C31 |
| prime radical | C31×#585 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C31 ◁ C22×C4×C31 ◁ G | |
704 conjugacy classes of subgroups; only the 212 normal subgroups are shown.
This group has 704 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)(32,33,38,43)(34,44,47,56)(35,40,49,55)(36,42,37,41)(39,50,53,46)(45,59,62,58)(48,57,51,54)(52,60,63,61);(32,34)(33,39)(35,45)(36,46)(37,50)(38,47)(40,52)(41,44)(42,56)(43,53)(48,60)(49,62)(51,61)(54,58)(55,63)(57,59);(32,35)(33,40)(34,45)(36,48)(37,51)(38,49)(39,52)(41,54)(42,57)(43,55)(44,58)(46,60)(47,62)(50,61)(53,63)(56,59);(32,36,38,37)(33,41,43,42)(34,46,47,50)(35,48,49,51)(39,44,53,56)(40,54,55,57)(45,60,62,61)(52,58,63,59)899 conjugacy classes — view the full character table.
| maximal subgroup of | C31×#13355, C31×#13356, C31×#13361, … |
| maximal normal subgroup of | C31×#13355, C31×#13356, C31×#13361, … |
| maximal quotient of | C31×#18136, C31×#18140, C31×#18146, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3968, 1754);