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×#3019 |
| 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 | |
762 conjugacy classes of subgroups; only the 212 normal subgroups are shown.
This group has 762 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) = 53 |
| transitive degree | μt(G) = 592 |
A minimal faithful permutation representation — 4 generators on 53 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)(40,46)(41,49)(42,44)(43,47)(45,51)(48,53)(50,52);(38,40)(39,43)(41,50)(42,48)(44,52)(45,53)(46,49)(47,51);(41,51)(45,49)(46,53)(47,50);(39,44)(43,52)(45,49)(46,53)1073 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C37×#23872, C37×#23873, C37×#23892, … |
| maximal normal subgroup of | C37×#23872, C37×#23873, C37×#23892, … |
| maximal quotient of | C37×#18132, C37×#18133, C37×#18137, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 1751);