Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23400 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C27 |
| direct product | C19×#23407 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
2106 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(25,30)(26,33)(27,28)(32,35)(34,36)(37,39);(20,21)(22,23)(24,25)(26,31)(27,35)(28,30)(29,32)(33,39)(34,38)(36,37);(21,23)(24,26)(25,31)(27,33)(28,36)(29,34)(30,37)(32,38)(35,39);(25,32)(30,35)(31,38)(37,39)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16395);