Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2212 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C37 · Schur multiplier (H2) = C22 |
| direct product | C37×#2212 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C37 | #459 |
| commutator, Frattini, cosocle | C2×C8 | C23×C37 |
| prime radical | C37×#509 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C37 ◁ C2×C4×C37 ◁ C4×C8×C37 ◁ G | |
154 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 154 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)(40,48)(41,53)(42,57)(43,59)(44,49)(45,51)(46,50)(47,58)(52,66)(54,65)(55,69)(56,61)(60,62)(63,67)(64,68);(38,40,42,51,44,52,58,43)(39,45,47,48,49,59,57,66)(41,50,54,67,56,68,55,60)(46,61,62,65,64,53,63,69);(38,41)(39,46)(40,50)(42,54)(43,60)(44,56)(45,61)(47,62)(48,65)(49,64)(51,67)(52,68)(53,59)(55,58)(57,63)(66,69)851 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C37×#2212, C37×#33594, C37×#33595, … |
| maximal normal subgroup of | C2×C37×#2212, C37×#33594, C37×#33595, … |
| maximal quotient of | C37×#12416, C37×#12417, C37×#12420, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 944);