Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2002 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C37 · Schur multiplier (H2) = C24 |
| direct product | C37×#2004 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C37 | #120 |
| commutator, Frattini, cosocle | C22×C4 | C23×C37 |
| prime radical | C37×#535 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C37 ◁ C22×C4×C37 ◁ G | |
394 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 1184 |
A minimal faithful permutation representation — 3 generators on 57 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)(40,41)(42,43)(44,50)(45,53)(46,49)(47,51)(48,55)(52,57)(54,56);(42,44,46,52)(43,47,49,56)(45,54,55,51)(48,57,53,50);(39,41)(45,55)(47,56)(48,53)(51,54)962 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C37×#2004, C37×#23399, C37×#23401, … |
| maximal normal subgroup of | C2×C37×#2004, C37×#23399, C37×#23401, … |
| maximal quotient of | C37×#9916, C37×#9918, C37×#9924, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 736);