Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1999 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C37 · Schur multiplier (H2) = C22 |
| direct product | C37×#2097 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C37 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C23×C37 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C37 ◁ C2×C42×C37 ◁ G | |
238 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 65 |
| transitive degree | μt(G) = 4736 |
A minimal faithful permutation representation — 3 generators on 65 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)(42,43,45,47)(44,48,49,46)(50,51,53,57,54,58,62,55)(52,59,60,64,61,65,63,56);(38,39)(40,41)(42,44,45,49)(43,46,47,48)(51,55)(53,62)(56,59)(57,58)(60,63)(64,65);(39,41)(50,52,54,61)(51,56,58,64)(53,63,62,60)(55,59,57,65)1184 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C37×#2097, C37×#23730, C37×#23732, … |
| maximal normal subgroup of | C2×C37×#2097, C37×#23730, C37×#23732, … |
| maximal quotient of | C37×#10664, C37×#10669, C37×#10675, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 829);