Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1468 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C37 · Schur multiplier (H2) = C2×C4 |
| direct product | C37×#1470 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C37 | C2×C22⋊C4 |
| commutator | C23 | C22×C4×C37 |
| Frattini, cosocle | C22×C4 | C23×C37 |
| prime radical | C23×C37 | C22×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C37 ◁ C2×C42×C37 ◁ G | |
204 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 69 |
| transitive degree | μt(G) = 2368 |
A minimal faithful permutation representation — 3 generators on 69 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)(38,39)(40,46,48,43)(41,44)(42,45)(47,52,53,50)(49,51)(54,55,57,60,58,61,64,67)(56,59,63,66,62,65,68,69);(38,40,42,48)(39,43,45,46)(41,47,49,53)(44,50,51,52)(54,56)(55,59)(57,63)(58,62)(60,66)(61,65)(64,68)(67,69);(38,41,42,49)(39,44,45,51)(40,47,48,53)(43,50,46,52)(56,62)(59,65)(63,68)(66,69)1184 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C37×#8476, C37×#8478, C37×#8485, … |
| maximal normal subgroup of | C37×#8476, C37×#8478, C37×#8485, … |
| maximal quotient of | C37×#7657, C37×#7660, C37×#7663, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 202);