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) = C22×C4 |
| direct product | C37×#1812 |
| 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 | |
260 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 260 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)(40,48)(41,52,54,45)(42,55)(43,47)(44,50)(46,56)(49,62,64,60)(51,61)(53,59,68,67)(57,63,66,69)(58,65);(38,40,42,50,43,51,56,65)(39,44,46,48,47,58,55,61)(41,49,53,63,54,64,68,69)(45,57,59,60,52,66,67,62);(38,41)(39,45)(40,49)(42,53)(43,54)(44,57)(46,59)(47,52)(48,60)(50,63)(51,64)(55,67)(56,68)(58,66)(61,62)(65,69)1184 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C37×#7227, C37×#7228, C37×#11867, … |
| maximal normal subgroup of | C37×#7227, C37×#7228, C37×#11867, … |
| maximal quotient of | C37×#8601, C37×#8602, C37×#8603, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 544);