Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18376 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18385 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#3505 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
1012 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)(20,21,26,23)(22,32,37,47)(24,30,25,39)(27,31,43,40)(28,34,33,35)(29,41,38,42)(36,46,51,44)(45,50,49,48);(20,22)(21,28)(23,33)(24,35)(25,34)(26,37)(27,36)(29,46)(30,47)(31,45)(32,39)(38,44)(40,49)(41,48)(42,50)(43,51);(20,23,26,21)(22,33,37,28)(24,38,25,29)(27,40,43,31)(30,42,39,41)(32,48,47,50)(34,46,35,44)(36,49,51,45);(20,24,26,25)(21,29,23,38)(22,34,37,35)(27,41,43,42)(28,44,33,46)(30,31,39,40)(32,45,47,49)(36,50,51,48)817 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11373);