Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2613 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C37 · Schur multiplier (H2) = C23×C4 |
| direct product | C37×#2660 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C37 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C37 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C37 ◁ G | |
448 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 232 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) = 4736 |
A minimal faithful permutation representation — 4 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)(42,43)(44,46)(45,47)(48,49)(50,51,54,52)(53,56,57,55);(38,39,40,41)(42,43,45,47)(44,46,49,48)(50,52,54,51)(53,55,57,56);(38,39)(40,41)(42,43)(44,48)(45,47)(46,49)(50,53,54,57)(51,55,52,56);(42,44,45,49)(43,46,47,48)1184 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C37×#10091, C37×#10093, C37×#10099, … |
| maximal normal subgroup of | C37×#10091, C37×#10093, C37×#10099, … |
| maximal quotient of | C37×#14276, C37×#14277, C37×#14282, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 1392);