Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1714 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C37 · Schur multiplier (H2) = C8 |
| direct product | C37×#1720 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C37 | #127 |
| commutator, Frattini, cosocle | C42 | C23×C37 |
| prime radical | #127×C37 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C37 ◁ C42×C37 ◁ G | |
186 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 72 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 — 3 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)(38,39,43,40)(41,42,45,44)(46,47,50,53)(48,54,56,61)(49,58,55,52)(51,59,60,57);(38,40,42,45,43,39,44,41)(46,48,55,59,50,56,49,57)(47,51,58,61,53,60,52,54);(38,41,42,40,43,45,44,39)(48,56)(51,60)(54,61)(57,59)962 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C37×#1720, C37×#19613, C37×#19619, … |
| maximal normal subgroup of | C2×C37×#1720, C37×#19613, C37×#19619, … |
| maximal quotient of | C37×#8821, C37×#9827, C37×#9828, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 452);