Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C37 · Schur multiplier (H2) = C22×C4 |
| direct product | C37×#1979 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C37 | #121 |
| commutator | C2×C4 | C22×C4×C37 |
| Frattini, cosocle | C22×C4 | C23×C37 |
| prime radical | C23×C37 | #41 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C37 ◁ C22×C4×C37 ◁ G | |
276 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 112 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)(42,43,47,52,48,51,46,60)(44,49,55,64,54,65,61,63)(45,56,58,66,59,70,57,50)(53,67,69,62,68,72,71,73);(38,39,40,41)(42,44,46,55,48,54,47,61)(43,49,52,63,51,65,60,64)(45,53,57,69,59,68,58,71)(50,62,56,67,66,73,70,72);(42,45,47,58,48,59,46,57)(43,50,60,70,51,66,52,56)(44,53,61,71,54,68,55,69)(49,62,64,72,65,73,63,67)1184 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C37×#13019, C37×#13020, C37×#13023, … |
| maximal normal subgroup of | C37×#13019, C37×#13020, C37×#13023, … |
| maximal quotient of | C37×#9669, C37×#9671, C37×#9725, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 711);