Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C37 · Schur multiplier (H2) = C25 |
| direct product | C37×#2327 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C37 | C24 |
| commutator | C22 | C23×C4×C37 |
| Frattini, cosocle | C23 | C24×C37 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C37 ◁ G | |
516 conjugacy classes of subgroups; only the 296 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 296 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)(39,41)(42,43,45,44)(47,51)(48,54)(49,57)(59,61);(42,44,45,43)(46,47)(48,55)(49,53)(50,51)(52,54)(56,61)(57,58)(59,60);(38,39,40,41)(46,48)(47,52)(49,56)(50,54)(51,55)(53,59)(57,60)(58,61);(46,49,50,57)(47,53,51,58)(48,56,54,60)(52,59,55,61)1628 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C37×#9100, C37×#9104, C37×#9296, … |
| maximal normal subgroup of | C37×#9100, C37×#9104, C37×#9296, … |
| maximal quotient of | C37×#13779, C37×#13786, C37×#13790, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 1059);