Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18414 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18441 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#3559 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
888 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1216 |
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)(20,21,24,28)(22,26,29,33)(23,25,31,27)(30,32,35,34)(37,42)(39,40)(43,50)(44,48)(45,46)(49,51);(21,25)(23,31)(26,32)(27,28)(30,35)(33,34)(36,37)(38,43)(39,42)(40,48)(41,44)(45,50)(46,49)(47,51);(20,22,24,29)(21,26,28,33)(23,30,31,35)(25,32,27,34)(36,38,41,47)(37,43,44,51)(39,46,40,45)(42,49,48,50);(22,29)(26,33)(30,35)(32,34)(36,39,41,40)(37,42,44,48)(38,45,47,46)(43,50,51,49)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11429);