Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2018 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C37 · Schur multiplier (H2) = C23 |
| direct product | C37×#2047 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C37 | #121 |
| commutator, Frattini, cosocle | C22×C4 | C23×C37 |
| prime radical | C23×C37 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C37 ◁ C22×C4×C37 ◁ G | |
256 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 84 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)(38,39)(40,41)(42,43,47,51)(44,52,55,67)(45,56,59,49)(46,60,62,50)(48,61,64,54)(53,69,57,68)(58,66,73,71)(63,70,65,72);(42,44,47,55)(43,48,51,64)(45,57,59,53)(46,61,62,54)(49,65,56,63)(50,67,60,52)(58,70,73,72)(66,68,71,69);(39,41)(42,45,46,58,47,59,62,73)(43,49,50,66,51,56,60,71)(44,53,54,70,55,57,61,72)(48,63,52,68,64,65,67,69)962 conjugacy classes — view the full character table.
| maximal subgroup of | C37×#12167, C37×#12168, C37×#12169, … |
| maximal normal subgroup of | C37×#12167, C37×#12168, C37×#12169, … |
| maximal quotient of | C37×#10446, C37×#10447, C37×#10454, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 779);