Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2812 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C37 · Schur multiplier (H2) = C2×C42 |
| direct product | C37×#2825 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C37 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C37 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C37 ◁ G | |
522 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 168 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)(43,45)(46,47)(48,51)(49,50)(52,53)(54,55,58,59)(56,60,61,57);(40,44)(43,45)(47,50)(48,52)(56,61)(57,60);(38,39)(40,43)(41,42)(44,45)(46,47)(48,53)(49,50)(51,52)(54,56)(55,57)(58,61)(59,60);(38,40)(39,43)(41,44)(42,45)(46,48)(47,51)(49,52)(50,53)(54,57)(55,56)(58,60)(59,61)962 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C37×#2825, C37×#36670, C37×#36676, … |
| maximal normal subgroup of | C2×C37×#2825, C37×#36670, C37×#36676, … |
| maximal quotient of | C37×#14621, C37×#14637, C37×#14642, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 1557);