Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2018 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C2×C19×#2089 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | #121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C24×C19 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C23×C4×C19 ◁ G | |
810 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2)(27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45);(3,4)(5,10)(6,8)(7,9)(11,12,14,19,16,20,15,18)(13,17,22,25,23,24,21,26);(3,5,7,6)(4,8,9,10)(11,13)(12,17)(14,22)(15,21)(16,23)(18,26)(19,25)(20,24);(3,6,7,5)(4,8,9,10)(12,18)(13,21)(14,15)(17,24)(19,20)(22,23)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16660);