Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2184 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C37 · Schur multiplier (H2) = C2 |
| direct product | C37×#2229 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C37 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C23×C37 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C37 ◁ C42×C37 ◁ C4×C8×C37 ◁ G | |
124 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 4736 |
A minimal faithful permutation representation — 3 generators on 77 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)(38,39,41,43)(40,44,45,42)(46,47,49,52)(48,56,57,74)(50,62,60,75)(51,65,61,55)(53,69,67,58)(54,71,68,64)(59,76,66,72)(63,73,77,70);(38,40,41,45)(39,42,43,44)(47,52)(53,67)(54,68)(55,65)(56,74)(62,75)(70,73)(72,76);(46,48,49,57)(47,53,52,67)(50,63,60,77)(51,66,61,59)(54,72,68,76)(55,73,65,70)(56,75,74,62)(58,71,69,64)1073 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C37×#2229, C37×#33626, C37×#33628, … |
| maximal normal subgroup of | C2×C37×#2229, C37×#33626, C37×#33628, … |
| maximal quotient of | C37×#12814, C37×#12936, C37×#12938, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 961);