Finite Group DatabasebetaFinite Group Databasebeta| order | 3968 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2010 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C31 · Schur multiplier (H2) = C22 |
| direct product | C31×#2098 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C31 | #127 |
| commutator, Frattini, cosocle | C22×C4 | C23×C31 |
| socle | C2×C31 | #399 |
| prime radical | C2×#41×C31 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C31 ◁ C22×C4×C31 ◁ G | |
210 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 80 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 — 3 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)(32,33,36,41,37,42,38,52)(34,43,45,55,47,59,46,39)(35,48,50,58,51,40,53,57)(44,60,49,63,61,56,62,54);(32,34,38,45,37,47,36,46)(33,39,52,43,42,55,41,59)(35,49,53,61,51,62,50,44)(40,56,58,54,48,60,57,63);(32,35)(33,40)(34,44)(36,50)(37,51)(38,53)(39,54)(41,57)(42,48)(43,60)(45,49)(46,62)(47,61)(52,58)(55,63)(56,59)806 conjugacy classes — view the full character table.
| maximal subgroup of | C31×#7438, C31×#7439, C31×#12301, … |
| maximal normal subgroup of | C31×#7438, C31×#7439, C31×#12301, … |
| maximal quotient of | C31×#10659, C31×#10660, C31×#10661, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3968, 830);