Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3055 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C37 · Schur multiplier (H2) = C23×C4 |
| direct product | C37×#3139 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C37 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C37 |
| prime radical | C23×C37 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C37 ◁ C2×C42×C37 ◁ G | |
380 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 192 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 — 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)(40,43)(41,42)(44,45)(46,47,52,57)(48,54,58,61)(49,53,59,60)(50,56,51,55);(39,42)(43,45)(46,48,51,59,52,58,50,49)(47,53,56,61,57,60,55,54);(38,40,41,44)(39,43,42,45)(46,49,50,58,52,59,51,48)(47,54,55,60,57,61,56,53);(48,58)(49,59)(53,60)(54,61)1184 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C37×#9422, C37×#9426, C37×#9436, … |
| maximal normal subgroup of | C37×#9422, C37×#9426, C37×#9436, … |
| maximal quotient of | C37×#20764, C37×#21094, C37×#21202, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 1871);