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) = C24 |
| direct product | C19×#11314 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #388 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| socle | C2×C19 | #1443 |
| prime radical | C24×C19 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C23×C4×C19 ◁ G | |
548 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)(20,21,25,30,26,29,24,31)(22,32,34,43,36,27,35,44)(23,37,40,46,41,47,39,28)(33,45,38,48,49,51,50,42);(20,22,24,34,26,36,25,35)(21,27,31,44,29,32,30,43)(23,38,39,49,41,50,40,33)(28,45,47,48,46,51,37,42);(20,23)(21,28,29,46)(22,33)(24,39)(25,40)(26,41)(27,42,32,48)(30,37,31,47)(34,38)(35,50)(36,49)(43,51,44,45)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4302);