Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2613 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C37 · Schur multiplier (H2) = C26 |
| direct product | C37×#2614 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C37 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C37 |
| prime radical | C22×D4×C37 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C37 ◁ G | |
782 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 782 conjugacy classes of subgroups — too many to draw. Only its 232 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 61 |
| transitive degree | μt(G) = 2368 |
A minimal faithful permutation representation — 4 generators on 61 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)(43,45)(46,47,50,53)(48,54,56,51)(49,52,58,57)(55,60,61,59);(39,41)(43,45)(46,48,50,56)(47,51,53,54)(49,55,58,61)(52,59,57,60);(38,39)(40,41)(42,43)(44,45)(46,47)(48,54)(49,57)(50,53)(51,56)(52,58)(55,59)(60,61);(46,49)(47,52)(48,55)(50,58)(51,59)(53,57)(54,60)(56,61)1184 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C37×#18225, C37×#18227, C37×#23905, … |
| maximal normal subgroup of | C37×#18225, C37×#18227, C37×#23905, … |
| maximal quotient of | C37×#14256, C37×#14263, C37×#14301, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 1346);