Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18562 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18589 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C19×#121 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
878 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 2432 |
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)(20,21,25,28)(22,29,31,34)(23,27,24,32)(26,33,35,30)(37,41)(38,44)(39,46)(43,47)(45,48)(49,51);(20,22)(21,26)(23,30)(24,33)(25,31)(27,34)(28,35)(29,32)(36,37,40,43)(38,42,45,50)(39,47,46,41)(44,49,48,51);(20,23,25,24)(21,27,28,32)(22,30,31,33)(26,34,35,29)(36,38,40,45)(37,42,43,50)(39,48,46,44)(41,49,47,51);(22,31)(26,35)(29,34)(30,33)(37,43)(41,47)(42,50)(49,51)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11577);