Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9303 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#9304 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #386 |
| commutator | C42 | C22×C4×C19 |
| Frattini, cosocle | C2×C42 | C23×C19 |
| prime radical | C23×C19 | #121 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
436 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 1216 |
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)(21,25)(22,23)(26,27)(28,29)(30,34,39,49)(31,41)(32,44)(33,36)(35,42)(37,46)(38,52,53,59)(40,56,55,48)(43,51)(45,50)(47,57,58,54);(20,21,23,25,24,27,22,26)(28,30)(29,34,36,49)(31,38)(32,40)(33,39)(35,47,50,58)(37,48,44,56)(41,52,51,59)(42,54)(43,53)(45,57)(46,55);(20,22,24,23)(21,26,27,25)(28,31,33,43)(29,35,36,50)(30,38,39,53)(32,45,46,42)(34,47,49,58)(37,51,44,41)(40,57,55,54)(48,59,56,52)931 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 2292);