Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#19570 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#121 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C19×#532 | C22 |
| 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)(21,25)(23,30)(26,31)(27,32)(29,34)(33,35)(36,37,41,44)(38,45,43,40)(39,46,47,51)(42,48,50,49);(20,21,23,25,24,27,30,32)(22,26,29,31,28,33,34,35)(36,38,40,37,41,43,45,44)(39,46,48,42,47,51,49,50);(20,22)(21,26)(23,29)(24,28)(25,31)(27,33)(30,34)(32,35)(36,39,41,47)(37,42,44,50)(38,46,43,51)(40,48,45,49);(21,27)(22,28)(25,32)(29,34)(39,47)(42,50)(46,51)(48,49)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 12558);