Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#19004 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
896 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)(21,26)(22,30)(23,24)(28,29)(31,32)(33,34)(37,42)(39,40)(43,50)(44,47)(45,48)(49,51);(20,21)(22,27)(23,28)(24,26)(25,29)(30,34)(31,35)(32,33)(36,37,41,44)(38,43,46,51)(39,42,40,47)(45,49,48,50);(20,22)(21,27)(23,30)(24,32)(25,31)(26,33)(28,34)(29,35)(36,38)(37,43)(39,45)(40,48)(41,46)(42,49)(44,51)(47,50);(20,23,25,24)(21,28,29,26)(22,30,31,32)(27,34,35,33)(36,39,41,40)(37,42,44,47)(38,45,46,48)(43,49,51,50)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11992);