Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2008 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C37 · Schur multiplier (H2) = C24 |
| direct product | C37×#2009 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C37 | #392 |
| commutator, Frattini, cosocle | C22×C4 | C23×C37 |
| prime radical | C37×#575 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C37 ◁ C22×C4×C37 ◁ G | |
348 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 88 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)(40,50)(41,54)(42,48)(43,47)(44,49)(45,52)(46,56)(51,59)(53,64)(55,63)(57,62)(58,60)(61,67)(65,66)(68,69);(38,40)(39,45)(41,51)(42,58)(43,52)(44,53)(46,61)(47,64)(48,50)(49,60)(54,65)(55,68)(56,66)(57,67)(59,63)(62,69);(38,41,44,57)(39,46,49,63)(40,51,53,67)(42,56,43,55)(45,59,60,61)(47,54,48,62)(50,65,64,69)(52,68,58,66)851 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C37×#2009, C37×#23412, C37×#23873, … |
| maximal normal subgroup of | C2×C37×#2009, C37×#23412, C37×#23873, … |
| maximal quotient of | C37×#9931, C37×#9933, C37×#9935, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 741);