Finite Group DatabasebetaFinite Group Databasebeta| order | 3968 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2613 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C31 · Schur multiplier (H2) = C25 |
| direct product | C31×#2622 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C31 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C31 |
| prime radical | C2×C31×#120 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C31 ◁ G | |
702 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 702 conjugacy classes of subgroups — too many to draw. Only its 200 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)(36,37)(38,41)(39,40)(42,43)(45,48)(49,50);(33,35)(37,40)(41,42)(44,45,47,48)(46,49,51,50);(32,33)(34,35)(36,37)(38,42)(39,40)(41,43)(44,45)(46,50)(47,48)(49,51);(36,38)(37,41)(39,43)(40,42)(44,46)(45,49)(47,51)(48,50)992 conjugacy classes — view the full character table.
| maximal subgroup of | C31×#24058, C31×#24114, C2×C31×#2622, … |
| maximal normal subgroup of | C31×#24058, C31×#24114, C2×C31×#2622, … |
| maximal quotient of | C31×#14255, C31×#14259, C31×#14262, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3968, 1354);