Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19651 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C23×C4 |
| direct product | C19×#19659 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#127 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C19×#532 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
700 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)(22,28)(23,25)(24,32)(26,30)(27,31)(29,34)(33,35)(36,37,41,44)(38,45,43,40)(39,47,48,46)(42,50,51,49);(21,25)(26,33)(27,32)(28,34)(36,38,40,37,41,43,45,44)(39,46,49,42,48,47,50,51);(20,22,24,30,23,29,31,35)(21,26,27,28,25,33,32,34)(36,39,40,49,41,48,45,50)(37,42,43,47,44,51,38,46);(39,48)(42,51)(46,47)(49,50)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 12647);