Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24398 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C23×C4 |
| direct product | C19×#24675 |
| 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 | |
764 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,26)(23,24)(25,27)(28,29,33,38,32,37,34,39)(30,40,43,55,42,35,49,51)(31,44,47,53,46,54,48,36)(41,57,45,50,58,52,59,56);(21,24)(25,26)(28,30)(29,35)(31,45)(32,42)(33,43)(34,49)(36,52)(37,40)(38,51)(39,55)(41,48)(44,56)(46,59)(47,58)(50,54)(53,57);(28,31,32,46)(29,36,37,53)(30,41,42,58)(33,48,34,47)(35,50,40,56)(38,54,39,44)(43,59,49,45)(51,57,55,52);(20,22,23,27)(21,25,24,26)(29,37)(35,40)(36,53)(38,39)(44,54)(50,56)(51,55)(52,57)817 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 17663);