Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18346 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24×C4 |
| direct product | C19×#18359 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#2631 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
1004 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)(21,26)(22,30)(23,35)(27,40)(28,38)(29,36)(31,46)(33,49)(34,45)(37,48)(39,42)(41,51)(43,47)(44,50);(20,21,24,29)(22,31,34,27)(23,36,35,26)(25,28,32,41)(30,43,45,42)(33,39,50,47)(37,51,48,38)(40,49,46,44);(23,37)(26,38)(33,44)(35,48)(36,51)(39,40)(46,47)(49,50);(20,22,32,45)(21,27,41,43)(23,33,48,49)(24,34,25,30)(26,39,51,46)(28,42,29,31)(35,50,37,44)(36,47,38,40)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11347);