Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3192 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C37 · Schur multiplier (H2) = C24 |
| direct product | C37×#3195 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C37 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C37 |
| prime radical | C24×C37 | D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C37 ◁ C23×C4×C37 ◁ G | |
410 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 176 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) = 1184 |
A minimal faithful permutation representation — 4 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)(40,44)(41,43)(42,45)(46,47,50,53)(48,54,55,61)(49,57,59,52)(51,58,60,56);(38,40)(39,42)(41,45)(43,44)(48,55)(51,60)(54,61)(56,58);(40,45)(42,44)(46,48,50,55)(47,51,53,60)(49,58,59,56)(52,61,57,54);(39,43)(42,44)962 conjugacy classes — view the full character table.
| maximal subgroup of | C37×#9342, C37×#9935, C37×#9937, … |
| maximal normal subgroup of | C37×#9342, C37×#9935, C37×#9937, … |
| maximal quotient of | C37×#21765, C37×#21942, C37×#22050, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 1927);