Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1999 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C2×C19×#2087 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C19 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C19 ◁ C22×C42×C19 ◁ G | |
1054 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 4864 |
A minimal faithful permutation representation — 4 generators on 41 points:
(1,2)(23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41);(7,8)(9,14)(10,12)(11,13)(15,16,19,20,18,22,17,21);(3,4)(5,6)(7,9,11,10)(8,12,13,14)(15,17,18,19)(16,20,22,21);(4,6)(7,10,11,9)(8,12,13,14)(16,21)(17,19)(20,22)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16653);