Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3026 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C37 · Schur multiplier (H2) = C26 |
| direct product | C37×#3028 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C37 | C2×#120 |
| commutator, Frattini, cosocle | C23 | C24×C37 |
| prime radical | C37×#585 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C37 ◁ C22×C4×C37 ◁ G | |
716 conjugacy classes of subgroups; only the 212 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 212 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 69 |
| transitive degree | μt(G) = 1184 |
A minimal faithful permutation representation — 4 generators on 69 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)(38,39,43,47)(40,44,50,57)(41,45,52,59)(42,53,54,46)(48,60,62,55)(49,63,64,56)(51,65,66,58)(61,67,69,68);(38,40)(39,44)(41,48)(42,49)(43,50)(45,55)(46,56)(47,57)(51,61)(52,62)(53,63)(54,64)(58,67)(59,60)(65,68)(66,69);(38,41)(39,45)(40,48)(42,51)(43,52)(44,55)(46,58)(47,59)(49,61)(50,62)(53,65)(54,66)(56,67)(57,60)(63,68)(64,69);(38,42,43,54)(39,46,47,53)(40,49,50,64)(41,51,52,66)(44,56,57,63)(45,58,59,65)(48,61,62,69)(55,67,60,68)1073 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C37×#13351, C37×#13352, C37×#13354, … |
| maximal normal subgroup of | C37×#13351, C37×#13352, C37×#13354, … |
| maximal quotient of | C37×#18308, C37×#18309, C37×#18310, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 1760);