Finite Group DatabasebetaFinite Group Databasebeta| order | 3968 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1999 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C31 · Schur multiplier (H2) = C22 |
| direct product | C31×#2097 |
| 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 | |
238 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 3968 |
A minimal faithful permutation representation — 3 generators on 59 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)(36,37,39,41)(38,42,43,40)(44,45,47,51,48,52,56,49)(46,53,54,58,55,59,57,50);(32,33)(34,35)(36,38,39,43)(37,40,41,42)(45,49)(47,56)(50,53)(51,52)(54,57)(58,59);(33,35)(44,46,48,55)(45,50,52,58)(47,57,56,54)(49,53,51,59)992 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C31×#2097, C31×#23730, C31×#23732, … |
| maximal normal subgroup of | C2×C31×#2097, C31×#23730, C31×#23732, … |
| maximal quotient of | C31×#10664, C31×#10669, C31×#10675, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3968, 829);