Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2032 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C37 · Schur multiplier (H2) = C23 |
| direct product | C37×#2032 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C37 | #393 |
| commutator, Frattini, cosocle | C24 | C23×C37 |
| prime radical | C22×D4×C37 | C22 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C37 ◁ C24×C37 ◁ G | |
278 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 592 |
A minimal faithful permutation representation — 3 generators on 53 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)(40,43)(41,48,50,44)(42,45)(46,53,49,51)(47,52);(38,40)(39,43)(41,49,50,46)(42,47)(44,51,48,53)(45,52);(38,41)(39,44)(40,46)(42,50)(43,51)(45,48)(47,49)(52,53)851 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C37×#2032, C37×#23474, C37×#23996, … |
| maximal normal subgroup of | C2×C37×#2032, C37×#23474, C37×#23996, … |
| maximal quotient of | C37×#10374, C37×#10375, C37×#10376, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 764);