Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1595 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C37 · Schur multiplier (H2) = C23 |
| direct product | C37×#1616 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C37 | #120 |
| commutator, Frattini, cosocle | C22×C4 | C23×C37 |
| prime radical | C37×#537 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C37 ◁ C22×C4×C37 ◁ G | |
246 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 68 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) = 1184 |
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)(38,39,41,44)(40,42,45,43)(46,47,50,53)(48,51,55,58)(49,52,56,59)(54,60,61,57);(39,42)(40,45)(43,44)(46,48)(47,51)(49,54)(50,55)(52,57)(53,58)(56,61)(59,60);(46,49,50,56)(47,52,53,59)(48,54,55,61)(51,57,58,60)851 conjugacy classes — view the full character table.
| maximal subgroup of | C37×#12127, C37×#12128, C37×#12129, … |
| maximal normal subgroup of | C37×#12127, C37×#12128, C37×#12129, … |
| maximal quotient of | C37×#7791, C37×#7795, C37×#7808, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 348);