Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18132 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18149 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C2×C19×#538 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
1074 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,26,30)(22,31,33,46)(23,28,36,45)(24,37,39,48)(25,29,35,44)(27,40,43,32)(34,41,47,51)(38,42,49,50);(20,22)(21,27)(23,32)(24,38)(25,34)(26,33)(28,41)(29,42)(30,43)(31,37)(35,47)(36,40)(39,49)(44,50)(45,51)(46,48);(20,23,35,39)(21,28,44,48)(22,32,47,49)(24,26,36,25)(27,41,50,46)(29,37,30,45)(31,43,51,42)(33,40,34,38);(21,29)(27,42)(28,37)(30,44)(31,41)(43,50)(45,48)(46,51)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11137);