Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C37 · Schur multiplier (H2) = C23 |
| direct product | C37×#2402 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C37 | C23 |
| commutator, Frattini, cosocle | C23 | C24×C37 |
| socle, prime radical | C23×C37 | C24 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C37 ◁ G | |
400 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 216 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)(38,39)(40,43)(41,42)(44,45)(46,47)(48,51)(49,53)(50,52)(54,55,57,59)(56,58,60,61);(39,42)(43,45)(46,48,50,49)(47,51,52,53)(54,56)(55,58)(57,60)(59,61);(46,49,50,48)(47,51,52,53)(56,60)(58,61);(38,40,41,44)(39,43,42,45)1628 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C37×#10372, C37×#10373, C37×#21676, … |
| maximal normal subgroup of | C37×#10372, C37×#10373, C37×#21676, … |
| maximal quotient of | C37×#13846, C37×#13848, C37×#13854, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 1134);