Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10304 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C22×C4 |
| direct product | C19×#10310 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | #127 |
| commutator, Frattini, cosocle | C2×C42 | C23×C19 |
| prime radical | C2×C19×#127 | C22 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C2×C42×C19 ◁ G | |
670 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,23)(25,29)(26,27)(30,31)(32,33,35,34)(36,37,39,38);(21,23)(24,25,28,31)(26,30,27,29)(32,34)(33,35)(36,38)(37,39);(25,29)(26,27)(30,31)(33,37)(34,38)(36,39)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3298);