Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#19001 |
| 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 | |
960 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)(22,30)(23,29)(24,28)(25,27)(26,31)(32,35)(33,34)(36,37)(38,44)(39,47)(40,42)(41,45)(43,49)(46,51)(48,50);(20,22)(21,26)(23,33)(24,31)(25,32)(27,34)(28,35)(29,30)(36,38,40,46)(37,41,42,50)(39,48,49,45)(43,51,47,44);(20,22)(21,26)(23,31)(24,33)(25,32)(27,34)(28,30)(29,35)(39,49)(43,47)(44,51)(45,48);(21,27)(26,34)(28,29)(30,35)(37,42)(41,50)(43,47)(44,51)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11989);