Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18376 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18411 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C23×C19 | C22×D4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
870 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)(20,21,25,29)(22,30,33,34)(23,28,24,27)(26,31,35,32)(37,41)(39,46)(42,50)(43,47)(44,48)(49,51);(20,22,25,33)(21,26,29,35)(23,32,24,31)(27,30,28,34)(36,37,40,43)(38,42,45,51)(39,47,46,41)(44,49,48,50);(36,38,40,45)(37,42,43,51)(39,48,46,44)(41,49,47,50);(20,23,25,24)(21,27,29,28)(22,31,33,32)(26,34,35,30)(37,43)(41,47)(42,51)(49,50)817 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11399);