Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18316 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18329 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C2×C19×#538 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
1078 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)(20,21,25,30)(22,32,35,41)(23,28,24,38)(26,31,36,29)(27,39,44,33)(34,48,49,47)(37,46,40,45)(42,50,43,51);(20,22)(21,27)(23,33)(24,39)(25,35)(26,34)(28,41)(29,42)(30,44)(31,43)(32,38)(36,49)(37,50)(40,51)(45,48)(46,47);(20,23,36,40)(21,28,29,45)(22,33,49,51)(24,26,37,25)(27,41,42,48)(30,38,31,46)(32,43,47,44)(34,50,35,39);(21,29)(27,42)(28,45)(30,31)(32,47)(38,46)(41,48)(43,44)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11317);