Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2812 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C37 · Schur multiplier (H2) = C2×C42 |
| direct product | C37×#2835 |
| 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 | |
380 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 168 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)(39,42)(43,45)(46,47)(48,50)(49,51)(52,53)(54,55,58,60)(56,57,59,61);(40,44)(43,45)(46,47,49,51)(48,50,53,52)(54,56)(55,57)(58,59)(60,61);(38,39,41,42)(40,43,44,45)(46,48,49,53)(47,50,51,52)(54,57)(55,59)(56,60)(58,61);(38,40)(39,43)(41,44)(42,45)(46,47)(48,52)(49,51)(50,53)962 conjugacy classes — view the full character table.
| maximal subgroup of | C37×#12139, C37×#12233, C2×C37×#2835, … |
| maximal normal subgroup of | C37×#12139, C37×#12233, C2×C37×#2835, … |
| maximal quotient of | C37×#14627, C37×#14635, C37×#14647, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 1567);