Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #11234 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#11389 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #391 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| socle | C2×C19 | #1446 |
| prime radical | C24×C19 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C23×C4×C19 ◁ G | |
836 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 3 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,26,31,40)(23,33)(24,36)(25,28)(27,35)(29,37)(30,43,45,48)(32,47,46,39)(34,49)(38,51,41,44)(42,50);(20,22)(21,26,28,40)(23,30)(24,32)(25,31)(27,41,42,38)(29,39,36,47)(33,48,49,43)(34,45)(35,44)(37,46)(50,51);(20,23)(21,27,28,42)(22,30)(24,35)(25,34)(26,38,40,41)(29,33,36,49)(31,45)(32,44)(37,50)(39,43,47,48)(46,51)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4377);