Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2812 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C37 · Schur multiplier (H2) = C24 |
| direct product | C37×#2822 |
| 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 | |
380 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 184 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 65 |
| transitive degree | μt(G) = 4736 |
A minimal faithful permutation representation — 4 generators on 65 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)(43,44)(47,48)(50,51,55,57)(52,58,60,53)(54,56,64,65)(59,63,62,61);(39,41)(42,43,46,44)(45,47,49,48)(50,52,55,60)(51,53,57,58)(54,62,64,59)(56,63,65,61);(38,39)(40,41)(42,44,46,43)(45,47,49,48)(50,53)(51,52)(54,63)(55,58)(56,62)(57,60)(59,65)(61,64);(42,45,46,49)(43,47,44,48)(50,54,55,64)(51,56,57,65)(52,59,60,62)(53,61,58,63)962 conjugacy classes — view the full character table.
| maximal subgroup of | C37×#10080, C37×#10084, C37×#10087, … |
| maximal normal subgroup of | C37×#10080, C37×#10084, C37×#10087, … |
| maximal quotient of | C37×#14629, C37×#14631, C37×#14634, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 1554);