Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18414 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24×C4 |
| direct product | C19×#18433 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#121 | C23 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
872 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)(23,30)(25,31)(26,33)(28,34)(36,37,42,39)(38,46,49,51)(40,45,41,44)(43,50,47,48);(20,21)(22,25)(23,26)(24,27)(28,32)(29,31)(30,33)(34,35)(36,38,42,49)(37,43,39,47)(40,48,41,50)(44,46,45,51);(20,22)(21,25)(23,28)(24,29)(26,32)(27,31)(30,34)(33,35)(36,39,42,37)(38,47,49,43)(40,44,41,45)(46,50,51,48);(20,23,24,30)(21,26,27,33)(22,28,29,34)(25,32,31,35)(36,40,42,41)(37,44,39,45)(38,48,49,50)(43,46,47,51)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11421);