Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1619 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C37 · Schur multiplier (H2) = C22 |
| direct product | C37×#1653 |
| 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 | |
194 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 194 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) = 61 |
| transitive degree | μt(G) = 4736 |
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)(46,47,51,55)(48,56,59,60)(49,52,50,54)(53,57,61,58);(38,39,41,43)(40,45,44,42)(47,52)(49,50)(53,60)(54,55)(56,61)(57,58);(46,48,51,59)(47,53,55,61)(49,58,50,57)(52,60,54,56)962 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C37×#1653, C37×#18503, C37×#18518, … |
| maximal normal subgroup of | C2×C37×#1653, C37×#18503, C37×#18518, … |
| maximal quotient of | C37×#7760, C37×#7761, C37×#7767, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 385);