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×#19726 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#127 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C19×#3184 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
724 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)(20,21,26,23)(22,29,33,35)(24,28,25,34)(27,31,30,32)(36,37,42,47)(38,44,49,50)(39,43,48,51)(40,45,41,46);(20,22,24,31,26,33,25,32)(21,27,34,35,23,30,28,29)(36,38,41,48,42,49,40,39)(37,43,45,50,47,51,46,44);(20,23,26,21)(22,30,33,27)(24,28,25,34)(29,32,35,31)(36,39,40,49,42,48,41,38)(37,44,46,51,47,50,45,43);(20,24,26,25)(21,28,23,34)(22,31,33,32)(27,29,30,35)(36,40,42,41)(37,45,47,46)(38,48,49,39)(43,44,51,50)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 12714);