Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2812 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C37 · Schur multiplier (H2) = C24 |
| direct product | C37×#2817 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C37 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C37 |
| prime radical | C24×C37 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C37 ◁ G | |
444 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 184 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 65 |
| transitive degree | μt(G) = 2368 |
A minimal faithful permutation representation — 4 generators on 65 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)(43,46)(47,49)(50,51,55,53)(52,58,60,56)(54,57,63,61)(59,65,62,64);(39,41)(43,46)(44,48)(50,52,55,60)(51,56,53,58)(54,62,63,59)(57,65,61,64);(38,39)(40,41)(42,43)(44,47)(45,46)(48,49)(50,53,55,51)(52,56,60,58)(54,57,63,61)(59,65,62,64);(42,44)(43,47)(45,48)(46,49)(50,54,55,63)(51,57,53,61)(52,59,60,62)(56,64,58,65)962 conjugacy classes — view the full character table.
| maximal subgroup of | C37×#9982, C37×#9985, C37×#12095, … |
| maximal normal subgroup of | C37×#9982, C37×#9985, C37×#12095, … |
| maximal quotient of | C37×#14626, C37×#14627, C37×#14629, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 1549);