Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16×C19 · Schur multiplier (H2) = C22 |
| direct product | C19×#13628 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C16×C19 | C23 |
| commutator | C22 | C22×C16×C19 |
| Frattini, cosocle | C2×C16 | C23×C19 |
| socle | C22×C19 | C22×C16 |
| prime radical | C23×C19 | C2×C16 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C16×C19 ◁ G | |
206 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 3 generators on 87 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,23)(24,25,27,32,28,33,40,50,29,34,41,51,43,53,62,72,30,35,42,52,44,54,63,73,45,55,64,74,65,75,80,85)(26,31,37,47,38,48,59,69,39,49,60,70,61,71,79,84,36,46,56,66,57,67,76,81,58,68,77,82,78,83,86,87);(20,21,22,23)(24,26)(25,31)(27,37)(28,38)(29,39)(30,36)(32,47)(33,48)(34,49)(35,46)(40,59)(41,60)(42,56)(43,61)(44,57)(45,58)(50,69)(51,70)(52,66)(53,71)(54,67)(55,68)(62,79)(63,76)(64,77)(65,78)(72,84)(73,81)(74,82)(75,83)(80,86)(85,87);(26,36)(31,46)(37,56)(38,57)(39,58)(47,66)(48,67)(49,68)(59,76)(60,77)(61,78)(69,81)(70,82)(71,83)(79,86)(84,87)2128 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6616);