Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #25196 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#25197 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2424 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
968 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)(20,21,25,29,26,30,24,38)(22,31,33,27,34,42,39,43)(23,35,36,45,37,44,40,28)(32,47,49,51,50,41,48,46);(20,22,25,33,26,34,24,39)(21,27,29,42,30,43,38,31)(23,32,36,49,37,50,40,48)(28,41,35,46,45,47,44,51);(20,23)(21,28)(22,32)(24,36)(25,40)(26,37)(27,41)(29,44)(30,45)(31,46)(33,48)(34,50)(35,38)(39,49)(42,51)(43,47);(20,21,26,30)(22,27,34,43)(23,28,37,45)(24,38,25,29)(31,33,42,39)(32,41,50,47)(35,40,44,36)(46,48,51,49)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 18185);