Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19328 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#19359 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#121 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C19×#121 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
584 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,25,29)(22,30,32,35)(23,28,24,27)(26,33,34,31)(37,42)(38,46)(39,40)(44,45)(47,48)(49,50);(36,37,39,44,41,45,40,42)(38,43,46,50,48,51,47,49);(20,22)(21,26)(23,31)(24,33)(25,32)(27,30)(28,35)(29,34)(36,38)(37,43)(39,46)(40,47)(41,48)(42,49)(44,50)(45,51);(20,23,25,24)(21,27,29,28)(22,31,32,33)(26,30,34,35)(36,39,41,40)(37,44,45,42)(38,47,48,46)(43,49,51,50)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 12347);