Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2081 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C37 · Schur multiplier (H2) = C22 |
| direct product | C37×#2082 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C37 | #397 |
| commutator, Frattini, cosocle | C22×C4 | C23×C37 |
| prime radical | C23×C37 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C37 ◁ C22×C4×C37 ◁ G | |
184 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 69 |
| transitive degree | μt(G) = 1184 |
A minimal faithful permutation representation — 3 generators on 69 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)(38,39,43,48,44,49,42,47)(40,50,53,45,54,61,52,62)(41,55,57,63,58,64,59,46)(51,66,67,69,56,60,68,65);(38,40,44,54)(39,45,49,62)(41,56,58,51)(42,53,43,52)(46,60,63,66)(47,61,48,50)(55,69,64,65)(57,67,59,68);(38,41,42,57,44,58,43,59)(39,46,47,55,49,63,48,64)(40,51,52,67,54,56,53,68)(45,60,50,65,62,66,61,69)851 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C37×#2082, C37×#23652, C37×#24987, … |
| maximal normal subgroup of | C2×C37×#2082, C37×#23652, C37×#24987, … |
| maximal quotient of | C37×#10632, C37×#10633, C37×#10635, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 814);