Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18524 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18536 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C19×#3109 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
940 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1216 |
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)(22,29)(23,27)(24,32)(25,28)(26,30)(31,34)(33,35)(36,37)(38,46)(39,42)(40,45)(41,44)(43,48)(47,51)(49,50);(20,22,25,31)(21,26,28,35)(23,30,24,33)(27,34,32,29)(37,42)(39,40)(43,50)(44,45)(46,51)(47,48);(20,23,25,24)(21,27,28,32)(22,30,31,33)(26,34,35,29)(36,38,41,49)(37,43,44,51)(39,48,40,47)(42,50,45,46);(21,28)(26,35)(27,32)(29,34)(37,44)(42,45)(43,51)(46,50)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11524);