Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23998 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#24001 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2404 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#3020 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
1122 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)(22,27)(23,34)(24,29)(25,40)(26,31)(28,38)(30,43)(32,48)(33,39)(35,51)(36,50)(37,47)(41,45)(42,46)(44,49);(20,22,26,29)(21,27,31,24)(23,35)(25,33,43,46)(28,44)(30,42,40,39)(32,37)(34,48)(36,45)(38,50)(41,49)(47,51);(20,23)(21,28)(22,32)(24,36)(25,41)(26,37)(27,44)(29,35)(30,47)(31,45)(33,50)(34,40)(38,43)(39,48)(42,51)(46,49);(20,24,26,27)(21,29,31,22)(23,36,37,44)(25,42,43,39)(28,35,45,32)(30,33,40,46)(34,49,47,50)(38,48,41,51)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16989);