Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9103 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#11156 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #386 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| prime radical | C24×C19 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
826 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 generators on 55 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(24,25,29,35,30,33,28,34)(26,36,39,46,40,31,38,47)(27,41,42,49,43,50,44,32)(37,51,52,45,53,55,54,48);(20,21)(22,23)(24,26,30,40)(25,31,33,36)(27,37,43,53)(28,39,29,38)(32,48,49,45)(34,47,35,46)(41,55,50,51)(42,54,44,52);(21,23)(24,27)(25,32,33,49)(26,37)(28,42)(29,44)(30,43)(31,45,36,48)(34,41,35,50)(38,52)(39,54)(40,53)(46,55,47,51)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4144);