Finite Group DatabasebetaFinite Group Databasebeta| order | 3968 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2846 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C31 · Schur multiplier (H2) = C23 |
| direct product | C31×#2863 |
| 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 | |
408 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 408 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)(32,33,37,36)(34,39,35,38)(40,41,44,47)(42,45,46,43)(50,54)(52,55);(32,34,37,35)(33,38,36,39)(40,42,44,46)(41,45,47,43)(48,49,51,53)(50,52,54,55);(32,35,37,34)(33,39,36,38)(40,43,44,45)(41,46,47,42);(32,36,37,33)(34,39,35,38)(40,41)(42,45)(43,46)(44,47)(48,50)(49,52)(51,54)(53,55)1364 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C31×#7669, C31×#7673, C31×#7689, … |
| maximal normal subgroup of | C31×#7669, C31×#7673, C31×#7689, … |
| maximal quotient of | C31×#14688, C31×#14699, C31×#14703, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3968, 1595);