Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3019 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C37 · Schur multiplier (H2) = C26 |
| direct product | C37×#3021 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C37 | C2×#120 |
| commutator, Frattini, cosocle | C2×C4 | C24×C37 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C37 ◁ C22×C4×C37 ◁ G | |
736 conjugacy classes of subgroups; only the 212 normal subgroups are shown.
This group has 736 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)(39,44)(41,42)(45,52)(46,49)(47,50)(51,53);(38,39)(40,45)(41,44)(42,49)(43,46)(47,51)(48,53)(50,52);(38,40)(39,45)(41,47)(42,50)(43,48)(44,51)(46,53)(49,52);(38,41,43,42)(39,44,46,49)(40,47,48,50)(45,51,53,52)1073 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C37×#13353, C37×#13354, C37×#13360, … |
| maximal normal subgroup of | C37×#13353, C37×#13354, C37×#13360, … |
| maximal quotient of | C37×#18135, C37×#18141, C37×#18145, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 1753);