Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #7318 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#7318 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #1304 |
| commutator | C22×C4 | C42×C19 |
| Frattini, cosocle | C22×#41 | C22×C19 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C23×C19 ◁ C22×#41×C19 ◁ G | |
484 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 2 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,24,28)(22,30,32,44)(23,27,34,41)(25,29,36,43)(26,37,38,31)(33,40,46,50)(35,42,47,51)(39,48,49,45);(20,22)(21,26)(23,31)(24,32,36,46)(25,33)(27,40)(28,38,43,49)(29,39)(30,42)(34,37,47,48)(35,45)(41,50,51,44)532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 306);