Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1655 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C37 · Schur multiplier (H2) = C22 |
| direct product | C37×#1663 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C37 | #120 |
| commutator, Frattini, cosocle | C42 | C23×C37 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C37 ◁ C42×C37 ◁ G | |
172 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 60 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) = 4736 |
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)(38,39,44,48)(40,49,51,52)(41,50,45,53)(42,47,43,46)(54,55,59,57)(56,62,65,69)(58,66,68,61)(60,67,63,64);(38,40)(39,45)(41,48)(42,53)(43,50)(44,51)(46,52)(47,49)(54,56,59,65)(55,60,57,63)(58,67,68,64)(61,69,66,62);(38,41,44,45)(39,40,48,51)(42,52,43,49)(46,50,47,53)(54,57,59,55)(56,63,65,60)(58,61,68,66)(62,67,69,64)740 conjugacy classes — view the full character table.
| maximal subgroup of | C37×#7526, C2×C37×#1663, C37×#18990, … |
| maximal normal subgroup of | C37×#7526, C2×C37×#1663, C37×#18990, … |
| maximal quotient of | C37×#7763, C37×#7768, C37×#7772, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 395);