Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2184 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C37 · Schur multiplier (H2) = C23 |
| direct product | C37×#2189 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C37 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C23×C37 |
| prime radical | C2×#135×C37 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C37 ◁ C22×C4×C37 ◁ C22×C8×C37 ◁ G | |
220 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 68 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 — 3 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)(42,43,48,52)(44,53,56,71)(45,50,47,62)(46,58,61,72)(49,64,67,55)(51,57,69,60)(54,70,63,68)(59,65,73,66);(42,44)(43,49)(45,54)(46,59)(47,63)(48,56)(50,65)(51,68)(52,67)(53,58)(55,60)(57,64)(61,73)(62,66)(69,70)(71,72);(39,41)(42,45,48,47)(43,50,52,62)(44,54,56,63)(46,57,61,60)(49,65,67,66)(51,58,69,72)(53,70,71,68)(55,59,64,73)1073 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C37×#2189, C37×#33516, C37×#33519, … |
| maximal normal subgroup of | C2×C37×#2189, C37×#33516, C37×#33519, … |
| maximal quotient of | C37×#12107, C37×#12163, C37×#12283, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 921);