Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C37 · Schur multiplier (H2) = C22×C4 |
| direct product | C37×#1971 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C37 | C2×D4 |
| commutator | C2×C4 | C22×C4×C37 |
| Frattini, cosocle | C22×C4 | C23×C37 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C37 ◁ C2×C42×C37 ◁ G | |
304 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 128 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) = 4736 |
A minimal faithful permutation representation — 3 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)(39,41)(42,43,44,45)(46,47)(48,56)(49,52)(50,59)(51,55)(53,57)(54,60)(58,61);(38,39,40,41)(43,45)(46,48,50,49,51,57,60,58)(47,52,54,56,55,61,59,53);(46,49,50,57,51,58,60,48)(47,53,54,52,55,56,59,61)1184 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C37×#7111, C37×#13026, C37×#13039, … |
| maximal normal subgroup of | C37×#7111, C37×#13026, C37×#13039, … |
| maximal quotient of | C37×#9658, C37×#9664, C37×#9720, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 703);