Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3026 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C37 · Schur multiplier (H2) = C25×C4 |
| direct product | C37×#3027 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C37 | C2×#120 |
| commutator, Frattini, cosocle | C23 | C24×C37 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C37 ◁ C22×C4×C37 ◁ G | |
772 conjugacy classes of subgroups; only the 212 normal subgroups are shown.
This group has 772 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) = 53 |
| transitive degree | μt(G) = 592 |
A minimal faithful permutation representation — 4 generators on 53 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)(41,48)(43,49)(44,51)(46,52);(38,39)(40,43)(41,44)(42,45)(46,50)(47,49)(48,51)(52,53);(38,40)(39,43)(41,46)(42,47)(44,50)(45,49)(48,52)(51,53);(38,41,42,48)(39,44,45,51)(40,46,47,52)(43,50,49,53)1073 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C37×#13350, C37×#13351, C37×#13353, … |
| maximal normal subgroup of | C37×#13350, C37×#13351, C37×#13353, … |
| maximal quotient of | C37×#18300, C37×#18301, C37×#18302, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 1759);