Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32870 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#32870 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2826 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#2018 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
502 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)(20,21,24,28,26,31,25,30)(22,32,35,27,36,42,33,43)(23,29,39,44,40,45,38,46)(34,47,49,41,37,50,48,51);(20,22,24,35,26,36,25,33)(21,27,30,32,31,43,28,42)(23,37,38,49,40,34,39,48)(29,41,44,50,45,51,46,47);(21,28)(22,33)(23,38)(24,25)(29,45)(30,31)(32,42)(34,37)(35,36)(39,40)(41,50)(47,51);(20,23)(21,29)(22,34)(24,39)(25,38)(26,40)(27,41)(28,44)(30,46)(31,45)(32,47)(33,48)(35,49)(36,37)(42,50)(43,51)532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 25858);