Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2668 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C37 · Schur multiplier (H2) = C2×C42 |
| direct product | C37×#2736 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C37 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C37 |
| prime radical | C25×C37 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C37 ◁ G | |
560 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 560 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)(41,42)(43,45)(46,47,50,51)(48,52,53,49)(54,55,57,59)(56,60,61,58);(39,42)(40,45)(47,51)(49,52)(54,55,57,59)(56,58,61,60);(38,40)(39,43)(41,45)(42,44)(46,48)(47,49)(50,53)(51,52)(54,55)(56,58)(57,59)(60,61);(38,39)(40,43)(41,42)(44,45)(46,49)(47,48)(50,52)(51,53)(54,56)(55,58)(57,61)(59,60)1184 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C37×#12188, C37×#12264, C37×#36725, … |
| maximal normal subgroup of | C37×#12188, C37×#12264, C37×#36725, … |
| maximal quotient of | C37×#14366, C37×#14481, C37×#14577, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 1468);