Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1468 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C37 · Schur multiplier (H2) = C2×C4 |
| direct product | C37×#1998 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C37 | C2×C22⋊C4 |
| commutator | C23 | C22×C4×C37 |
| Frattini, cosocle | C22×C4 | C23×C37 |
| prime radical | C23×C37 | C22×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C37 ◁ C2×C42×C37 ◁ G | |
228 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 112 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 — 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)(40,44)(41,42)(43,45)(46,47,50,53,49,52,54,60)(48,51,56,59,55,58,57,61);(39,42)(43,44)(46,48,54,56,49,55,50,57)(47,51,53,61,52,58,60,59);(38,40,41,45)(39,43,42,44)(47,52)(51,58)(53,60)(59,61)1184 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C37×#8485, C37×#8486, C37×#10497, … |
| maximal normal subgroup of | C37×#8485, C37×#8486, C37×#10497, … |
| maximal quotient of | C37×#9880, C37×#9881, C37×#9892, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 730);