Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3019 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C37 · Schur multiplier (H2) = C26 |
| direct product | C37×#3020 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C37 | C2×#120 |
| commutator, Frattini, cosocle | C2×C4 | C24×C37 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C37 ◁ C22×C4×C37 ◁ G | |
698 conjugacy classes of subgroups; only the 212 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 212 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 — 4 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)(42,54)(43,46)(44,50)(47,57)(49,65)(51,62)(52,63)(53,60)(55,59)(56,61)(58,66)(64,67)(68,69);(38,40)(39,44)(41,49)(42,55)(43,51)(45,58)(46,59)(47,62)(48,54)(50,57)(52,68)(53,67)(56,66)(60,69)(61,64)(63,65);(38,41,43,53)(39,45,46,60)(40,49,51,67)(42,56,57,52)(44,58,59,69)(47,63,54,61)(48,64,62,65)(50,68,55,66);(39,46)(44,59)(45,60)(47,54)(48,62)(58,69)(61,63)(64,65)1073 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C37×#23874, C37×#23875, C37×#23893, … |
| maximal normal subgroup of | C37×#23874, C37×#23875, C37×#23893, … |
| maximal quotient of | C37×#18134, C37×#18139, C37×#18142, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 1752);