Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #25140 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#25142 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#525 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
986 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)(20,21)(22,23)(24,25,28,32,29,33,42,49)(26,30,35,44,36,45,53,55)(27,37,39,47,40,48,41,31)(34,50,51,46,38,54,52,43);(21,23)(24,26,28,35,29,36,42,53)(25,30,32,44,33,45,49,55)(27,38,39,52,40,34,41,51)(31,46,37,54,47,43,48,50);(24,27,29,40)(25,31,33,47)(26,34,36,38)(28,41,42,39)(30,43,45,46)(32,48,49,37)(35,52,53,51)(44,54,55,50);(21,23)817 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 18130);