Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2221 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C37 · Schur multiplier (H2) = C22 |
| direct product | C37×#2223 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C37 | #466 |
| commutator, Frattini, cosocle | C2×C8 | C23×C37 |
| prime radical | C37×#472 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C37 ◁ C2×C4×C37 ◁ #131×C37 ◁ G | |
144 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 60 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)(39,45)(40,51)(41,54)(42,43)(46,55)(47,62)(48,59)(49,58)(50,60)(52,67)(53,56)(57,63)(64,69)(65,68);(38,39,46,58,43,49,41,45,44,50,54,59,42,48,55,60)(40,47,61,69,51,63,52,57,53,64,66,62,56,65,67,68);(38,40)(39,47)(41,52)(42,56)(43,51)(44,53)(45,57)(46,61)(48,65)(49,63)(50,64)(54,66)(55,67)(58,69)(59,62)(60,68)962 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C37×#2223, C37×#33617, C37×#33618, … |
| maximal normal subgroup of | C2×C37×#2223, C37×#33617, C37×#33618, … |
| maximal quotient of | C37×#12432, C37×#12435, C37×#12441, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 955);