Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2192 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C37 · Schur multiplier (H2) = C23 |
| direct product | C37×#2194 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C37 | #447 |
| commutator, Frattini, cosocle | C2×C8 | C23×C37 |
| prime radical | C37×#576 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C37 ◁ C2×C4×C37 ◁ #131×C37 ◁ G | |
216 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 64 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)(38,39,44,50)(40,51,54,67)(41,55,59,66)(42,49,43,48)(45,61,64,52)(46,60,65,53)(47,57,62,58)(56,68,69,63);(38,40)(39,45)(41,56)(42,53)(43,60)(44,54)(46,62)(47,65)(48,63)(49,68)(50,64)(51,55)(52,58)(57,61)(59,69)(66,67);(38,40)(39,46)(41,52)(42,60)(43,53)(44,54)(45,62)(47,64)(48,67)(49,51)(50,65)(55,68)(56,58)(57,69)(59,61)(63,66)851 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C37×#2194, C37×#33538, C37×#33539, … |
| maximal normal subgroup of | C2×C37×#2194, C37×#33538, C37×#33539, … |
| maximal quotient of | C37×#12111, C37×#12113, C37×#12167, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 926);