Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19328 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#19365 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#121 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C19×#121 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
584 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)(22,30)(23,29)(24,26)(25,28)(27,31)(32,35)(33,34)(36,37,41,43)(38,40,45,50)(39,46,49,44)(42,48,51,47);(21,26)(27,34)(28,29)(30,35)(36,38,40,43,41,45,50,37)(39,44,48,51,49,46,47,42);(20,22)(21,27)(23,31)(24,32)(25,33)(26,34)(28,30)(29,35)(36,39)(37,42)(38,44)(40,48)(41,49)(43,51)(45,46)(47,50);(20,23,24,25)(21,28,26,29)(22,31,32,33)(27,30,34,35)(36,40,41,50)(37,38,43,45)(39,47,49,48)(42,46,51,44)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 12353);