Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1999 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C37 · Schur multiplier (H2) = C24 |
| direct product | C37×#2016 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C37 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C23×C37 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C37 ◁ C2×C42×C37 ◁ G | |
370 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 116 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)(38,39)(40,41)(46,47,52,56)(48,57,49,60)(50,55,51,54)(53,59,61,58);(39,41)(42,43)(44,45)(46,48,52,49)(47,53,56,61)(50,59,51,58)(54,60,55,57);(43,45)(46,49,52,48)(47,53,56,61)(50,58,51,59)(54,60,55,57)1184 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C37×#7405, C37×#7756, C37×#7757, … |
| maximal normal subgroup of | C37×#7405, C37×#7756, C37×#7757, … |
| maximal quotient of | C37×#9957, C37×#9959, C37×#9967, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 748);