Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2018 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C37 · Schur multiplier (H2) = C24 |
| direct product | C37×#2019 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C37 | #121 |
| commutator, Frattini, cosocle | C22×C4 | C23×C37 |
| prime radical | C2×AGL(1,ℤ/8)×C37 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C37 ◁ C22×C4×C37 ◁ G | |
362 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 1184 |
A minimal faithful permutation representation — 3 generators on 57 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)(42,43,46,50)(44,51,54,56)(45,48,55,49)(47,52,57,53);(39,41)(42,44)(43,47)(45,52)(46,54)(48,51)(49,56)(50,57)(53,55);(43,48)(44,52)(45,55)(49,50)(51,56)(53,54)962 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C37×#2019, C37×#23438, C37×#23439, … |
| maximal normal subgroup of | C2×C37×#2019, C37×#23438, C37×#23439, … |
| maximal quotient of | C37×#9975, C37×#9978, C37×#9987, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 751);