Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18562 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18601 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C22×D4×C19 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
910 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)(20,21,25,28)(22,29,32,35)(23,27,24,33)(26,30,34,31)(36,37,41,45)(38,46,47,50)(39,44,40,43)(42,49,51,48);(20,22,25,32)(21,26,28,34)(23,31,24,30)(27,35,33,29)(36,38,41,47)(37,42,45,51)(39,49,40,48)(43,50,44,46);(37,43)(39,40)(42,50)(44,45)(46,51)(48,49);(20,23,25,24)(21,27,28,33)(22,30,32,31)(26,29,34,35)(38,47)(42,51)(46,50)(48,49)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11589);