Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19713 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C23×C4 |
| direct product | C19×#19722 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#127 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
746 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)(26,31)(30,34)(32,35)(36,37)(38,47)(39,43)(40,45)(41,50)(42,46)(44,48)(49,51);(20,22,23,30,25,32,24,31)(21,26,33,35,28,34,27,29)(36,38,40,49,42,48,41,39)(37,43,50,44,46,51,45,47);(20,21)(22,26)(23,33)(24,27)(25,28)(29,31)(30,35)(32,34)(36,39,41,48,42,49,40,38)(37,44,45,43,46,47,50,51);(20,23,25,24)(21,27,28,33)(22,30,32,31)(26,29,34,35)(36,40,42,41)(37,45,46,50)(38,39,48,49)(43,44,51,47)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 12710);