Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9519 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#9529 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #386 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C2×C42 | C23×C19 |
| prime radical | C19×#3109 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
468 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,25)(22,29)(23,26)(28,33)(30,31)(32,34)(36,37,39,43,41,45,40,44)(38,46,47,42,48,50,49,51);(20,21,26,33,24,28,23,25)(22,27,29,34,31,35,30,32)(36,38)(37,42,45,51)(39,47)(40,49)(41,48)(43,50,44,46);(20,22)(21,27)(23,30)(24,31)(25,32)(26,29)(28,35)(33,34)(37,43)(39,40)(42,50)(44,45)(46,51)(47,49)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 2517);