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×#2483 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C31 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C31 |
| prime radical | C25×C31 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C31 ◁ G | |
700 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 700 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) = 51 |
| transitive degree | μt(G) = 992 |
A minimal faithful permutation representation — 4 generators on 51 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)(33,35)(36,37,40,38)(39,42,43,41)(45,48)(46,50);(37,38)(41,42)(44,45)(46,49)(47,48)(50,51);(32,33)(34,35)(36,38,40,37)(39,42,43,41)(44,46,47,50)(45,49,48,51);(36,39)(37,41)(38,42)(40,43)(44,45)(46,49)(47,48)(50,51)1178 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C31×#9500, C31×#9502, C31×#10338, … |
| maximal normal subgroup of | C31×#9500, C31×#9502, C31×#10338, … |
| maximal quotient of | C31×#13869, C31×#13992, C31×#14040, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3968, 1215);