Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2403 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C37 · Schur multiplier (H2) = C22×C4 |
| direct product | C37×#2607 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C37 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C37 |
| prime radical | C24×C37 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C37 ◁ G | |
444 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 444 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) = 2368 |
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)(46,47)(48,52)(49,50)(51,53)(54,55,58,57)(56,60,61,59);(39,42)(43,45)(47,50)(51,52)(56,61)(59,60);(38,39)(40,43)(41,42)(44,45)(46,47)(48,51)(49,50)(52,53)(54,56,58,61)(55,59,57,60);(38,40,41,44)(39,43,42,45)(46,48)(47,51)(49,53)(50,52)(54,57,58,55)(56,60,61,59)1406 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C37×#10386, C37×#10387, C37×#12121, … |
| maximal normal subgroup of | C37×#10386, C37×#10387, C37×#12121, … |
| maximal quotient of | C37×#13953, C37×#14091, C37×#14093, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 1339);