Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18414 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18414 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
1042 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
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)(21,26)(22,30)(23,33)(27,39)(28,37)(29,34)(31,43)(32,46)(35,48)(38,41)(40,50)(42,49)(44,45)(47,51);(20,21)(22,27)(23,34)(24,29)(25,28)(26,33)(30,41)(31,40)(32,47)(35,49)(36,42)(37,48)(38,45)(39,46)(43,51)(44,50);(22,31)(23,35)(26,37)(27,40)(30,43)(32,46)(33,48)(34,49)(38,50)(39,47)(41,51)(44,45);(20,22)(21,27)(23,32)(24,31)(25,30)(26,38)(28,41)(29,40)(33,45)(34,47)(35,44)(36,43)(37,39)(42,51)(46,48)(49,50)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11402);