Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3003 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C37 · Schur multiplier (H2) = C24 |
| direct product | C37×#3080 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C37 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C37 |
| prime radical | C2×#41×C37 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C37 ◁ C2×C42×C37 ◁ G | |
384 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 200 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 61 |
| transitive degree | μt(G) = 2368 |
A minimal faithful permutation representation — 4 generators on 61 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)(38,39,41,43)(40,44,45,42)(46,47,50,52)(48,56,58,61)(49,55,51,54)(53,59,60,57);(38,40,41,45)(39,42,43,44)(47,52)(53,60)(54,55)(56,61);(46,48)(47,53)(49,57)(50,58)(51,59)(52,60)(54,56)(55,61);(46,49,50,51)(47,54,52,55)(48,57,58,59)(53,56,60,61)1184 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C37×#9351, C37×#9352, C37×#24724, … |
| maximal normal subgroup of | C37×#9351, C37×#9352, C37×#24724, … |
| maximal quotient of | C37×#20649, C37×#20875, C37×#21034, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 1812);