Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#20318 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C2×D4×C19 | C2×D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C42×C19 ◁ G | |
556 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)(20,21,25,23)(22,28,31,35)(24,33,34,27)(26,29,32,30)(36,37)(38,44)(39,47)(40,42)(41,46)(43,49)(45,51)(48,50);(20,22,25,31)(21,26,23,32)(24,29,34,30)(27,35,33,28)(38,45)(41,50)(44,51)(46,48);(20,23,25,21)(22,26,31,32)(24,33,34,27)(28,29,35,30)(36,38,40,45)(37,41,42,50)(39,48,49,46)(43,51,47,44);(22,29)(24,34)(26,35)(27,33)(28,32)(30,31)(37,42)(41,50)(43,47)(44,51)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 13306);