Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2613 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C37 · Schur multiplier (H2) = C23 |
| direct product | C37×#2647 |
| 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 | |
360 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 360 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) = 61 |
| transitive degree | μt(G) = 4736 |
A minimal faithful permutation representation — 4 generators on 61 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)(39,40)(43,44)(46,47)(48,51)(49,52)(50,53)(54,55,58,56)(57,60,61,59);(38,39,42,40)(41,43,45,44)(46,48)(47,49)(50,52)(51,53)(54,56,58,55)(57,59,61,60);(38,40,42,39)(41,43,45,44)(46,48)(47,51)(49,53)(50,52)(54,57,58,61)(55,59,56,60);(38,41,42,45)(39,43,40,44)(46,49,50,51)(47,52,53,48)1184 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C37×#29133, C37×#29134, C37×#29135, … |
| maximal normal subgroup of | C37×#29133, C37×#29134, C37×#29135, … |
| maximal quotient of | C37×#14266, C37×#14276, C37×#14277, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 1379);