Finite Group DatabasebetaFinite Group Databasebeta| order | 3968 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C31 · Schur multiplier (H2) = C23 |
| direct product | C31×#2402 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C31 | C23 |
| commutator, Frattini, cosocle | C23 | C24×C31 |
| socle, prime radical | C23×C31 | C24 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C31 ◁ G | |
400 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 400 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)(34,37)(35,36)(38,39)(40,41)(42,45)(43,47)(44,46)(48,49,51,53)(50,52,54,55);(33,36)(37,39)(40,42,44,43)(41,45,46,47)(48,50)(49,52)(51,54)(53,55);(40,43,44,42)(41,45,46,47)(50,54)(52,55);(32,34,35,38)(33,37,36,39)1364 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C31×#10372, C31×#10373, C31×#21676, … |
| maximal normal subgroup of | C31×#10372, C31×#10373, C31×#21676, … |
| maximal quotient of | C31×#13846, C31×#13848, C31×#13854, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3968, 1134);