Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3057 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C37 · Schur multiplier (H2) = C25 |
| direct product | C37×#3059 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C37 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C37 |
| prime radical | C2×#41×C37 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C37 ◁ C2×#41×C37 ◁ G | |
460 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 200 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 73 |
| transitive degree | μt(G) = 2368 |
A minimal faithful permutation representation — 4 generators on 73 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)(40,41)(42,43,47,51)(44,52,56,66)(45,49,57,63)(46,59,53,50)(48,60,62,55)(54,65,68,73)(58,70,67,64)(61,71,72,69);(42,44,53,60,47,56,46,55)(43,48,59,66,51,62,50,52)(45,54,67,71,57,68,58,69)(49,61,70,73,63,72,64,65);(39,41)(42,45)(43,49)(44,54)(46,58)(47,57)(48,61)(50,64)(51,63)(52,65)(53,67)(55,69)(56,68)(59,70)(60,71)(62,72)(66,73);(45,57)(49,63)(54,68)(58,67)(61,72)(64,70)(65,73)(69,71)1184 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C37×#11869, C37×#11871, C37×#13075, … |
| maximal normal subgroup of | C37×#11869, C37×#11871, C37×#13075, … |
| maximal quotient of | C37×#19188, C37×#19193, C37×#19199, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 1791);