Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2846 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C37 · Schur multiplier (H2) = C24 |
| direct product | C37×#2859 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C37 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C37 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C37 ◁ G | |
472 conjugacy classes of subgroups; only the 264 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 264 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)(39,41)(44,47)(45,49)(50,51,55,54)(52,57,56,53);(42,43,46,48)(44,45,47,49)(50,52)(51,53)(54,57)(55,56);(38,39,40,41)(42,44,46,47)(43,45,48,49)(50,53,55,57)(51,56,54,52);(42,45)(43,47)(44,48)(46,49)(50,54,55,51)(52,57,56,53)1628 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C37×#7660, C37×#7663, C37×#7680, … |
| maximal normal subgroup of | C37×#7660, C37×#7663, C37×#7680, … |
| maximal quotient of | C37×#14687, C37×#14699, C37×#14707, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 1591);