Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2403 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C37 · Schur multiplier (H2) = C25 |
| direct product | C37×#2551 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C37 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C37 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C37 ◁ G | |
556 conjugacy classes of subgroups; only the 280 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 280 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) = 4736 |
A minimal faithful permutation representation — 4 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)(39,40)(46,47,50,53)(48,52,49,51);(38,39,41,40)(42,43,44,45)(46,48,50,49)(47,51,53,52);(42,43)(44,45)(46,48,50,49)(47,51,53,52);(38,40,41,39)(46,49,50,48)(47,52,53,51)1406 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C37×#10348, C37×#10349, C37×#10350, … |
| maximal normal subgroup of | C37×#10348, C37×#10349, C37×#10350, … |
| maximal quotient of | C37×#13910, C37×#14005, C37×#14053, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 1283);