Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#26782 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C22×D4×C19 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C4×C4⋊C4×C19 ◁ G | |
706 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)(20,21,23,24)(22,25,26,27)(28,29)(30,33)(31,32)(34,35)(36,37)(38,45)(39,49)(40,43)(41,44)(42,48)(46,50)(47,51);(21,24)(25,27)(36,38,40,48)(37,42,43,45)(39,47,41,46)(44,51,49,50);(20,22,23,26)(21,25,24,27)(29,32)(33,35)(37,43)(38,46)(39,41)(42,50)(45,51)(47,48);(21,24)(25,27)(28,30,31,34)(29,33,32,35)(36,39,40,41)(37,44,43,49)(38,47,48,46)(42,51,45,50)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 19770);