Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9519 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#9532 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #386 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C2×C42 | C23×C19 |
| prime radical | C19×#447 | C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
444 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1216 |
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)(20,21,23,26,25,29,24,28)(22,30,31,27,32,34,33,35)(36,37,42,45)(38,41,44,40)(39,46)(43,47)(48,50)(49,51);(21,26,29,28)(27,34,35,30)(36,38,40,37,42,44,41,45)(39,46,48,43,49,51,47,50);(20,22)(21,27)(23,31)(24,33)(25,32)(26,34)(28,30)(29,35)(36,39)(37,43)(38,46)(40,48)(41,47)(42,49)(44,51)(45,50)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 2520);