Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18376 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24×C4 |
| direct product | C19×#18389 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#2541 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
1170 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,25)(22,23)(26,27)(29,32)(30,34)(33,35);(20,21,24,27)(22,25,23,26)(28,29,31,33)(30,35,34,32);(30,34)(32,35);(20,22,24,23)(21,26,27,25)(29,33)(32,35)817 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11377);