Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #11115 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#11179 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #388 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| socle | C2×C19 | #1440 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C23×C4×C19 ◁ G | |
804 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)(20,21,25,29,26,31,24,30)(22,32,34,27,36,43,35,44)(23,37,39,47,40,46,41,28)(33,49,50,45,51,42,38,48);(20,22)(21,27)(23,38)(24,35)(25,34)(26,36)(28,45)(29,43)(30,32)(31,44)(33,39)(37,42)(40,50)(41,51)(46,49)(47,48);(20,23,24,39,26,40,25,41)(21,28,29,46,31,47,30,37)(22,33,34,38,36,51,35,50)(27,42,32,48,44,49,43,45)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4167);