Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#19038 |
| 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 | |
876 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)(22,29)(23,24)(28,31)(30,32)(33,35)(36,37)(38,45)(39,43)(40,49)(41,44)(42,47)(46,50)(48,51);(20,21)(22,27)(23,31)(24,26)(25,28)(29,35)(30,34)(32,33)(36,38)(37,42)(39,47)(40,46)(41,48)(43,51)(44,50)(45,49);(20,22)(21,27)(23,29)(24,32)(25,30)(26,33)(28,34)(31,35)(36,37)(38,42)(39,43)(40,49)(41,44)(45,46)(47,51)(48,50);(21,28)(26,31)(27,34)(33,35)(36,39,41,40)(37,43,44,49)(38,46,48,47)(42,45,50,51)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 12026);