Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #7457 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×#7457 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #1368 |
| commutator | C16 | C2×C8×C19 |
| Frattini, cosocle | #346 | C22×C19 |
| prime radical | C22×C19 | #365 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C2×C4×C19 ◁ C4×C8×C19 ◁ C19×#346 ◁ G | |
76 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 2 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,26,27,36,29,38,41,39)(22,30,31,44)(23,33)(24,35)(28,42,40,37,43,50,49,51)(32,47,46,45)(34,48);(20,21,22,26,23,28,30,37,24,27,32,39,33,40,45,42,25,29,31,38,34,43,44,51,35,41,46,36,48,49,47,50)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 445);