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×#18429 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#3561 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
932 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)(36,37,41,45)(38,46,48,51)(39,44,40,43)(42,49,50,47);(20,21)(22,25)(23,26)(24,27)(28,32)(29,31)(30,33)(34,35)(36,38,41,48)(37,42,45,50)(39,47,40,49)(43,46,44,51);(20,22)(21,25)(23,28)(24,29)(26,32)(27,31)(30,34)(33,35)(39,40)(43,44)(46,51)(47,49);(20,23,24,30)(21,26,27,33)(22,28,29,34)(25,32,31,35)(36,39,41,40)(37,43,45,44)(38,47,48,49)(42,46,50,51)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11417);