Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2199 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C37 · Schur multiplier (H2) = C23 |
| direct product | C37×#2201 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C37 | B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×D4 | C23×C37 |
| prime radical | H(5,𝔽2)×C37 | C22 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C37 ◁ C22×C37 ◁ C2×D4×C37 ◁ G | |
226 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 56 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)(40,48)(41,45)(42,46)(43,47)(44,50)(49,65)(51,64)(52,63)(53,59)(54,60)(55,62)(56,66)(57,67)(58,68)(61,69);(38,40,43,51)(39,44,47,57)(41,52,54,49)(42,50,55,67)(45,58,60,56)(46,48,62,64)(53,68,69,66)(59,63,61,65);(38,41,43,54)(39,45,47,60)(40,49,51,52)(42,53,55,69)(44,56,57,58)(46,61,62,59)(48,63,64,65)(50,66,67,68)629 conjugacy classes — view the full character table.
| maximal subgroup of | C37×#13679, C37×#13680, C2×C37×#2201, … |
| maximal normal subgroup of | C37×#13679, C37×#13680, C2×C37×#2201, … |
| maximal quotient of | C37×#12095, C37×#12101, C37×#12125, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 933);