Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2230 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C37 · Schur multiplier (H2) = C2 |
| direct product | C37×#2231 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C37 | #476 |
| commutator, Frattini, cosocle | C2×C8 | C23×C37 |
| prime radical | #135×C37 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C37 ◁ C2×C4×C37 ◁ C4×C8×C37 ◁ G | |
120 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 120 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) = 69 |
| transitive degree | μt(G) = 1184 |
A minimal faithful permutation representation — 3 generators on 69 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)(38,39,44,49)(40,50,53,48)(41,54)(42,58,51,47)(43,45,60,62)(46,63)(52,66)(55,68)(56,67)(57,61)(59,64)(65,69);(38,40,51,60,44,53,42,43)(39,45,58,48,49,62,47,50)(41,52,56,69,57,63,55,59)(46,61,65,67,66,54,64,68);(38,41)(39,46)(40,52)(42,55)(43,59)(44,57)(45,61)(47,64)(48,67)(49,66)(50,68)(51,56)(53,63)(54,62)(58,65)(60,69)851 conjugacy classes — view the full character table.
| maximal subgroup of | C37×#12463, C37×#12464, C37×#12465, … |
| maximal normal subgroup of | C37×#12463, C37×#12464, C37×#12465, … |
| maximal quotient of | C37×#12824, C37×#12950, C37×#13116, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 963);