Finite Group DatabasebetaFinite Group Databasebeta| order | 3968 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2403 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C31 · Schur multiplier (H2) = C24 |
| direct product | C31×#2571 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C31 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C31 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C31 ◁ G | |
380 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 216 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 — 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)(41,43)(45,46)(48,49,52,55)(50,54,51,53);(33,34)(37,38)(40,41,44,43)(42,45,47,46)(48,50,52,51)(49,53,55,54);(32,34,36,33)(35,38,39,37)(40,42,44,47)(41,45,43,46)(48,49)(50,53)(51,54)(52,55);(32,35,36,39)(33,37,34,38)(40,43,44,41)(42,46,47,45)(48,51,52,50)(49,54,55,53)1178 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C31×#10351, C31×#10352, C31×#10353, … |
| maximal normal subgroup of | C31×#10351, C31×#10352, C31×#10353, … |
| maximal quotient of | C31×#13911, C31×#13982, C31×#14030, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3968, 1303);