Finite Group DatabasebetaFinite Group Databasebeta| order | 3968 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1999 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C31 · Schur multiplier (H2) = C23 |
| direct product | C31×#2056 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C31 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C23×C31 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C31 ◁ C2×C42×C31 ◁ G | |
288 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 104 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 3968 |
A minimal faithful permutation representation — 3 generators on 55 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)(34,35)(40,41,45,49)(42,47,51,55)(43,52,50,46)(44,54,53,48);(36,37)(38,39)(40,42,45,51)(41,46,49,52)(43,53,50,44)(47,48,55,54);(33,35)(37,39)(40,43,44,42,45,50,53,51)(41,47,48,52,49,55,54,46)992 conjugacy classes — view the full character table.
| maximal subgroup of | C31×#7082, C31×#7090, C31×#12161, … |
| maximal normal subgroup of | C31×#7082, C31×#7090, C31×#12161, … |
| maximal quotient of | C31×#10478, C31×#10479, C31×#10482, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3968, 788);