Finite Group DatabasebetaFinite Group Databasebeta| order | 3968 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2846 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C31 · Schur multiplier (H2) = C24 |
| direct product | C31×#2859 |
| 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 | |
472 conjugacy classes of subgroups; only the 264 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 264 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) = 3968 |
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)(38,41)(39,43)(44,45,49,48)(46,51,50,47);(36,37,40,42)(38,39,41,43)(44,46)(45,47)(48,51)(49,50);(32,33,34,35)(36,38,40,41)(37,39,42,43)(44,47,49,51)(45,50,48,46);(36,39)(37,41)(38,42)(40,43)(44,48,49,45)(46,51,50,47)1364 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C31×#7660, C31×#7663, C31×#7680, … |
| maximal normal subgroup of | C31×#7660, C31×#7663, C31×#7680, … |
| maximal quotient of | C31×#14687, C31×#14699, C31×#14707, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3968, 1591);