Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2668 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C37 · Schur multiplier (H2) = C23×C4 |
| direct product | C37×#2804 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C37 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C37 |
| prime radical | C22×D4×C37 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C37 ◁ G | |
480 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 192 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)(39,42)(40,44)(46,47,49,50)(48,51,52,53)(54,55)(56,59)(57,58)(60,61);(39,42)(43,45)(47,50)(48,52)(55,57)(56,60);(38,39)(40,43)(41,42)(44,45)(46,47)(48,51)(49,50)(52,53)(54,56,58,60)(55,59,57,61);(38,40,41,44)(39,43,42,45)(46,48)(47,51)(49,52)(50,53)(54,57,58,55)(56,61,60,59)1184 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C37×#7745, C37×#7755, C37×#7782, … |
| maximal normal subgroup of | C37×#7745, C37×#7755, C37×#7782, … |
| maximal quotient of | C37×#14440, C37×#14457, C37×#14471, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 1536);