Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9331 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#9339 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #386 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C2×C42 | C23×C19 |
| prime radical | C19×#121 | C2×C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
416 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 3 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,25,24,22,27,26)(28,29)(30,39)(31,43,46,53)(32,47)(33,37)(34,38)(35,41)(36,45,52,44)(40,55,57,49)(42,50)(48,51)(54,56,59,58);(20,22)(21,24)(23,25)(26,27)(28,30,32,41,34,42,33,48)(29,35,37,39,38,51,47,50)(31,40,45,58,46,57,44,56)(36,49,53,54,52,55,43,59);(20,21)(22,24)(23,25)(26,27)(28,31)(29,36)(30,40)(32,45)(33,44)(34,46)(35,49)(37,53)(38,52)(39,54)(41,58)(42,57)(43,47)(48,56)(50,59)(51,55)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 2327);