Finite Group DatabasebetaFinite Group Databasebeta| order | 3968 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2812 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C31 · Schur multiplier (H2) = C24 |
| direct product | C31×#2822 |
| 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 | |
380 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 184 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 3968 |
A minimal faithful permutation representation — 4 generators on 59 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)(37,38)(41,42)(44,45,49,51)(46,52,54,47)(48,50,58,59)(53,57,56,55);(33,35)(36,37,40,38)(39,41,43,42)(44,46,49,54)(45,47,51,52)(48,56,58,53)(50,57,59,55);(32,33)(34,35)(36,38,40,37)(39,41,43,42)(44,47)(45,46)(48,57)(49,52)(50,56)(51,54)(53,59)(55,58);(36,39,40,43)(37,41,38,42)(44,48,49,58)(45,50,51,59)(46,53,54,56)(47,55,52,57)806 conjugacy classes — view the full character table.
| maximal subgroup of | C31×#10080, C31×#10084, C31×#10087, … |
| maximal normal subgroup of | C31×#10080, C31×#10084, C31×#10087, … |
| maximal quotient of | C31×#14629, C31×#14631, C31×#14634, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3968, 1554);