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×#3020 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C31 | C2×#120 |
| commutator, Frattini, cosocle | C2×C4 | C24×C31 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C31 ◁ C22×C4×C31 ◁ G | |
698 conjugacy classes of subgroups; only the 212 normal subgroups are shown.
This group has 698 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)(34,42)(35,39)(36,48)(37,40)(38,44)(41,51)(43,59)(45,56)(46,57)(47,54)(49,53)(50,55)(52,60)(58,61)(62,63);(32,34)(33,38)(35,43)(36,49)(37,45)(39,52)(40,53)(41,56)(42,48)(44,51)(46,62)(47,61)(50,60)(54,63)(55,58)(57,59);(32,35,37,47)(33,39,40,54)(34,43,45,61)(36,50,51,46)(38,52,53,63)(41,57,48,55)(42,58,56,59)(44,62,49,60);(33,40)(38,53)(39,54)(41,48)(42,56)(52,63)(55,57)(58,59)899 conjugacy classes — view the full character table.
| maximal subgroup of | C31×#23874, C31×#23875, C31×#23893, … |
| maximal normal subgroup of | C31×#23874, C31×#23875, C31×#23893, … |
| maximal quotient of | C31×#18134, C31×#18139, C31×#18142, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3968, 1752);