Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2184 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C37 · Schur multiplier (H2) = C4 |
| direct product | C37×#2234 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C37 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C23×C37 |
| prime radical | C37×#466 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C37 ◁ C22×C4×C37 ◁ C22×C8×C37 ◁ G | |
142 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 61 |
| transitive degree | μt(G) = 2368 |
A minimal faithful permutation representation — 3 generators on 61 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)(40,43)(41,42)(44,45)(47,51)(48,54)(50,57)(52,60)(53,56)(55,61)(58,59);(39,42)(43,45)(46,47,49,51)(48,52,55,59)(50,53,56,57)(54,58,61,60);(38,40,41,44)(39,43,42,45)(46,48,49,55)(47,52,51,59)(50,58,56,60)(53,61,57,54)1073 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C37×#2234, C37×#33645, C37×#33647, … |
| maximal normal subgroup of | C2×C37×#2234, C37×#33645, C37×#33647, … |
| maximal quotient of | C37×#12868, C37×#12921, C37×#12992, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 966);