Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23439 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#23603 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C24×C19 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
970 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 generators on 55 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(24,25,30,33,29,34,28,42)(26,35,44,46,37,52,38,31)(27,32,43,48,41,49,40,50)(36,51,54,45,53,47,39,55);(20,21)(22,23)(24,26,28,38,29,37,30,44)(25,31,33,35,34,46,42,52)(27,39,40,53,41,54,43,36)(32,47,48,55,49,51,50,45);(21,23)(24,27,29,41)(25,32,34,49)(26,36,37,53)(28,43,30,40)(31,45,46,55)(33,50,42,48)(35,51,52,47)(38,54,44,39);(26,37)(31,46)(35,52)(36,53)(38,44)(39,54)(45,55)(47,51)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16591);