Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1812 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C37 · Schur multiplier (H2) = C23 |
| direct product | C37×#1813 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C37 | #117 |
| commutator | C2×C4 | C22×C4×C37 |
| Frattini, cosocle | C22×C4 | C23×C37 |
| socle | C2×C37 | #380 |
| prime radical | C2×#41×C37 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C37 ◁ C2×M16×C37 ◁ G | |
252 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 116 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) = 1184 |
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)(38,39,43,47,44,48,42,57)(40,49,52,60,53,64,51,45)(41,54,55,61,56,46,58,62)(50,65,66,69,67,63,68,59);(38,40,42,51,44,53,43,52)(39,45,47,49,48,60,57,64)(41,50,55,66,56,67,58,68)(46,59,61,63,54,69,62,65);(38,41)(39,46)(40,50)(42,55)(43,58)(44,56)(45,59)(47,61)(48,54)(49,63)(51,66)(52,68)(53,67)(57,62)(60,69)(64,65)1184 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C37×#7227, C37×#7229, C37×#11870, … |
| maximal normal subgroup of | C37×#7227, C37×#7229, C37×#11870, … |
| maximal quotient of | C37×#8601, C37×#8602, C37×#8603, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 545);