Finite Group DatabasebetaFinite Group Databasebeta| order | 3968 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2668 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C31 · Schur multiplier (H2) = C43 |
| direct product | C31×#2785 |
| 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 | |
428 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 176 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)(32,33,36,34)(35,38,39,37)(40,41)(42,45)(43,44)(46,47)(49,50)(53,54);(33,34)(35,39)(41,43)(45,46)(48,49,52,50)(51,54,55,53);(32,34,36,33)(35,38,39,37)(40,42,44,47)(41,45,43,46)(48,50,52,49)(51,54,55,53);(32,35,36,39)(33,37,34,38)(40,43,44,41)(42,46,47,45)(48,51)(49,53)(50,54)(52,55)992 conjugacy classes — view the full character table.
| maximal subgroup of | C31×#12145, C31×#12239, C31×#36796, … |
| maximal normal subgroup of | C31×#12145, C31×#12239, C31×#36796, … |
| maximal quotient of | C31×#14399, C31×#14476, C31×#14589, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3968, 1517);