Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C37 · Schur multiplier (H2) = C24 |
| direct product | C37×#2399 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C37 | C23 |
| commutator, Frattini, cosocle | C23 | C24×C37 |
| socle, prime radical | C23×C37 | C24 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C37 ◁ G | |
504 conjugacy classes of subgroups; only the 248 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 248 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 4736 |
A minimal faithful permutation representation — 4 generators on 57 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)(42,43,46,49)(44,48,45,47)(50,51,54,57)(52,56,53,55);(38,39)(40,41)(42,44,46,45)(43,47,49,48)(50,52,54,53)(51,55,57,56);(39,41)(42,44,46,45)(43,48,49,47)(50,53,54,52)(51,56,57,55);(42,45,46,44)(43,47,49,48)1628 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C37×#9030, C37×#10014, C37×#10017, … |
| maximal normal subgroup of | C37×#9030, C37×#10014, C37×#10017, … |
| maximal quotient of | C37×#13848, C37×#13850, C37×#13856, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 1131);