Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24472 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#24475 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2410 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#3585 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
1324 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)(20,21,25,32,27,33,26,31)(22,34,38,47,39,49,37,28)(23,40,43,30,24,44,42,29)(35,45,41,48,50,51,36,46);(20,22)(21,28)(23,41)(24,36)(25,38)(26,37)(27,39)(29,48)(30,46)(31,49)(32,34)(33,47)(35,42)(40,51)(43,50)(44,45);(20,23,27,24)(21,29,33,30)(22,35,39,50)(25,42,26,43)(28,45,47,51)(31,40,32,44)(34,46,49,48)(36,37,41,38);(20,24,27,23)(21,30,33,29)(22,36,39,41)(25,42,26,43)(28,46,47,48)(31,40,32,44)(34,45,49,51)(35,37,50,38)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 17463);