Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2031 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C37 · Schur multiplier (H2) = C2 |
| direct product | C37×#2102 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C37 | #124 |
| commutator, Frattini, cosocle | C22×C4 | C23×C37 |
| socle | C2×C37 | #400 |
| prime radical | C23×C37 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C37 ◁ C22×C4×C37 ◁ G | |
158 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 158 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) = 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)(38,39,42,41,43,45,47,51)(40,46,48,53,49,50,52,44);(38,40,47,48,43,49,42,52)(39,44,51,46,45,53,41,50);(38,41,42,45,43,51,47,39)(40,46,48,53,49,50,52,44)962 conjugacy classes — view the full character table.
| maximal subgroup of | C37×#7440, C37×#7441, C37×#12307, … |
| maximal normal subgroup of | C37×#7440, C37×#7441, C37×#12307, … |
| maximal quotient of | C37×#10687, C37×#10688, C37×#10689, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 834);