Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2215 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C37 · Schur multiplier (H2) = C2×C4 |
| direct product | C37×#2249 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C37 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C23×C37 |
| prime radical | C2×D16×C37 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C37 ◁ C42×C37 ◁ C4×C8×C37 ◁ G | |
184 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 73 |
| transitive degree | μt(G) = 2368 |
A minimal faithful permutation representation — 3 generators on 73 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)(39,41)(42,43)(44,52)(45,57)(46,49)(47,60)(48,54)(50,53)(51,58)(55,64)(56,71)(59,72)(61,70)(62,73)(63,68)(65,67)(66,69);(42,44,53,67,47,56,59,70,46,55,68,73,58,69,45,54)(43,48,57,66,51,62,63,64,49,61,72,71,60,65,50,52);(38,39,40,41)(43,49)(48,61)(50,63)(51,60)(52,64)(57,72)(62,65)(66,71)1406 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C37×#7446, C37×#7447, C37×#13689, … |
| maximal normal subgroup of | C37×#7446, C37×#7447, C37×#13689, … |
| maximal quotient of | C37×#12503, C37×#12504, C37×#12505, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 981);