Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2002 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C37 · Schur multiplier (H2) = C24 |
| direct product | C37×#2005 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C37 | #120 |
| commutator, Frattini, cosocle | C22×C4 | C23×C37 |
| prime radical | C2×#41×C37 | C22 |
| 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)(44,52)(45,49)(46,55)(47,51)(48,53)(50,56)(54,57);(42,44,47,45)(43,48,51,57)(46,54,56,53)(49,55,52,50);(39,41)(42,45,47,44)(43,49,51,52)(46,53,56,54)(48,50,57,55)962 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C37×#2005, C37×#23399, C37×#23401, … |
| maximal normal subgroup of | C2×C37×#2005, C37×#23399, C37×#23401, … |
| maximal quotient of | C37×#9917, C37×#9919, C37×#9925, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 737);