Finite Group DatabasebetaFinite Group Databasebeta| order | 3968 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2613 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C31 · Schur multiplier (H2) = C23 |
| direct product | C31×#2643 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C31 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C31 |
| prime radical | C22×D4×C31 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C31 ◁ G | |
462 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 184 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) = 1984 |
A minimal faithful permutation representation — 4 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)(32,33,36,37)(34,35,38,39)(41,44)(45,46)(48,49)(50,53)(51,54)(52,55);(33,37)(34,38)(40,41,43,44)(42,45,47,46)(48,50)(49,52)(51,55)(53,54);(32,34)(33,35)(36,38)(37,39)(40,41)(42,46)(43,44)(45,47)(48,50)(49,53)(51,55)(52,54);(32,35)(33,38)(34,37)(36,39)(40,42)(41,45)(43,47)(44,46)(48,49)(50,52)(51,54)(53,55)992 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C31×#2643, C31×#34570, C31×#34584, … |
| maximal normal subgroup of | C2×C31×#2643, C31×#34570, C31×#34584, … |
| maximal quotient of | C31×#14259, C31×#14265, C31×#14331, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3968, 1375);