Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24398 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#24775 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C2×C19×AGL(1,ℤ/8) | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
850 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 generators on 55 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,22)(24,25,29,34,28,33,30,35)(26,36,39,51,38,31,45,47)(27,40,43,49,42,50,44,32)(37,53,41,46,54,48,55,52);(20,21,23,22)(24,26,28,38)(25,31,33,36)(27,41,42,55)(29,39,30,45)(32,48,49,53)(34,47,35,51)(37,43,54,44)(40,52,50,46);(24,27,28,42)(25,32,33,49)(26,37,38,54)(29,44,30,43)(31,46,36,52)(34,50,35,40)(39,55,45,41)(47,53,51,48);(20,22,23,21)(25,33)(31,36)(32,49)(34,35)(40,50)(46,52)(47,51)(48,53)817 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 17763);