Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#19155 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | #121 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| socle | C22×C19 | C2×#121 |
| prime radical | C19×#532 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C2×C42×C19 ◁ G | |
608 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)(22,29)(23,27)(24,33)(25,28)(26,32)(30,35)(31,34)(36,37)(38,44)(39,41)(40,48)(42,46)(43,47)(45,51)(49,50);(20,22,24,32,25,30,23,31)(21,26,27,29,28,34,33,35)(37,41)(42,50)(43,48)(44,51);(22,30)(26,34)(29,35)(31,32)(36,38,39,45)(37,42,41,50)(40,49,47,46)(43,51,48,44);(20,23,25,24)(21,27,28,33)(22,31,30,32)(26,29,34,35)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 12143);