Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2069 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#11138 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #396 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| socle | C2×C19 | #1439 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C23×C4×C19 ◁ G | |
864 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)(22,30)(23,34,37,27)(24,38)(25,29)(26,32)(28,40)(31,47,35,45)(33,46)(36,43,39,44)(41,49,51,48)(42,50);(20,22,24,32,25,33,40,50)(21,26,28,30,29,42,38,46)(23,35,36,49,37,31,39,48)(27,41,43,47,34,51,44,45);(20,23)(21,27)(22,31)(24,39)(25,37)(26,41)(28,44)(29,34)(30,45)(32,49)(33,35)(36,40)(38,43)(42,51)(46,47)(48,50)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4126);