Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19697 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C23×C4 |
| direct product | C19×#19705 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#127 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C2×C19×#127 | C22 |
| 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) = 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)(22,29)(23,27)(24,33)(25,28)(26,31)(30,34)(32,35)(36,37,40,43)(38,44,45,51)(39,47,48,42)(41,49,50,46);(20,22,24,31,25,32,23,30)(21,26,27,29,28,34,33,35)(38,45)(41,50)(44,51)(46,49);(20,21)(22,26)(23,33)(24,27)(25,28)(29,31)(30,35)(32,34)(36,38,39,46,40,45,48,49)(37,41,42,44,43,50,47,51);(20,23,25,24)(21,27,28,33)(22,30,32,31)(26,29,34,35)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 12693);