Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32696 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#32696 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2749 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#535 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
552 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)(20,21,24,29,25,28,39,45)(22,30,33,46,32,26,38,41)(23,34,37,50,36,27,42,44)(31,47,35,49,48,40,51,43);(20,22)(21,26)(23,35)(24,38)(25,32)(27,43)(28,30)(29,46)(31,37)(33,39)(34,49)(36,51)(40,44)(41,45)(42,48)(47,50);(20,23)(21,27,28,34)(22,31,32,48)(24,37)(25,36)(26,40)(29,44,45,50)(30,47)(33,35,38,51)(39,42)(41,43)(46,49);(21,28)(24,39)(27,34)(33,38)(35,51)(37,42)(41,46)(43,49)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 25684);