Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18974 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C19×#3546 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
930 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)(22,27)(23,28)(24,33)(25,29)(26,30)(31,34)(32,35)(36,37,41,44)(38,46,47,50)(39,42,40,45)(43,48,51,49);(20,22)(21,26)(23,30)(24,32)(25,31)(27,33)(28,34)(29,35)(37,42)(39,40)(43,50)(44,45)(46,51)(48,49);(20,22)(21,27)(23,32)(24,30)(25,31)(26,33)(28,35)(29,34)(36,38)(37,43)(39,49)(40,48)(41,47)(42,50)(44,51)(45,46);(20,23,25,24)(21,28,29,33)(22,30,31,32)(26,34,35,27)(37,44)(38,47)(42,45)(48,49)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11962);