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×#24525 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
858 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)(23,25)(24,27)(28,29,32,37,34,39,33,38)(30,35,41,50,43,52,42,51)(31,44,48,36,47,55,46,54)(40,56,45,49,58,53,57,59);(20,22,23,27)(21,24,25,26)(28,30)(29,35)(31,45)(32,41)(33,42)(34,43)(36,53)(37,50)(38,51)(39,52)(40,46)(44,49)(47,57)(48,58)(54,56)(55,59);(28,31)(29,36)(30,40)(32,46)(33,48)(34,47)(35,49)(37,44)(38,55)(39,54)(41,57)(42,45)(43,58)(50,56)(51,53)(52,59);(21,25)(24,26)(28,32,34,33)(29,37,39,38)(30,41,43,42)(31,46,47,48)(35,50,52,51)(36,44,54,55)(40,57,58,45)(49,56,59,53)817 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 17513);