Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1619 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C37 · Schur multiplier (H2) = C2×C4 |
| direct product | C37×#1634 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C37 | #120 |
| commutator, Frattini, cosocle | C42 | C23×C37 |
| prime radical | C37×#555 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C37 ◁ C42×C37 ◁ G | |
218 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 61 |
| transitive degree | μt(G) = 2368 |
A minimal faithful permutation representation — 3 generators on 61 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37)(39,42)(40,44)(43,45)(46,47,51,54)(48,55,57,60)(49,53,50,58)(52,59,61,56);(40,44)(42,45)(46,48,51,57)(47,52,54,61)(49,56,50,59)(53,60,58,55);(38,39,41,43)(40,45,44,42)(46,49,51,50)(47,53,54,58)(48,56,57,59)(52,60,61,55)962 conjugacy classes — view the full character table.
| maximal subgroup of | C37×#7521, C37×#13682, C2×C37×#1634, … |
| maximal normal subgroup of | C37×#7521, C37×#13682, C2×C37×#1634, … |
| maximal quotient of | C37×#7758, C37×#7760, C37×#7785, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 366);