Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2048 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C37 · Schur multiplier (H2) = C23 |
| direct product | C37×#2049 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C37 | #394 |
| commutator, Frattini, cosocle | C22×C4 | C23×C37 |
| prime radical | C2×#41×C37 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C37 ◁ C22×C4×C37 ◁ G | |
254 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 254 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) = 69 |
| transitive degree | μt(G) = 1184 |
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)(38,39,44,49)(40,50,53,65)(41,54,58,63)(42,48,43,47)(45,59,61,52)(46,56,64,57)(51,62,55,60)(66,69,68,67);(38,40)(39,45)(41,55)(42,59)(43,52)(44,53)(46,62)(47,65)(48,50)(49,61)(51,58)(54,68)(56,67)(57,69)(60,64)(63,66);(38,41,42,56,44,58,43,57)(39,46,47,63,49,64,48,54)(40,51,52,67,53,55,59,69)(45,60,50,66,61,62,65,68)851 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C37×#2049, C37×#23525, C37×#24295, … |
| maximal normal subgroup of | C2×C37×#2049, C37×#23525, C37×#24295, … |
| maximal quotient of | C37×#10444, C37×#10445, C37×#10446, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 781);