Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13417 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#13417 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2041 |
| commutator, Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C19×#3155 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ C19×#405 ◁ G | |
454 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)(22,34)(23,28)(24,40)(25,31)(26,30)(27,33)(29,37)(32,42)(35,45)(36,48)(38,46)(39,50)(41,47)(43,49)(44,51);(21,28)(22,35)(23,26)(24,25)(29,46)(30,33)(31,50)(34,49)(36,37)(38,41)(39,42)(43,44)(45,48)(47,51);(20,22,23,36,27,38,26,44)(21,29,30,47,33,49,28,45)(24,41,39,37,42,35,25,43)(31,48,32,34,50,51,40,46)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6405);