Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17597 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#17621 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C22×D4×C19 | D4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C4×D4×C19 ◁ G | |
990 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,26,28,41)(22,31)(23,35)(27,43,44,49)(29,42,30,36)(32,34)(37,39)(40,46,51,45);(20,21,24,29)(22,27,31,45)(23,36,35,41)(25,30,38,28)(26,39,42,37)(32,44,34,46)(33,49,47,51)(40,48,43,50);(20,22)(21,27)(23,33)(24,31)(25,34)(26,40)(28,44)(29,45)(30,46)(32,38)(35,47)(36,49)(37,50)(39,48)(41,51)(42,43);(22,32)(27,44)(31,34)(33,48)(40,51)(43,49)(45,46)(47,50)931 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 10609);