Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#19007 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C22×D4×C19 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
862 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)(20,21,24,26)(22,28,30,35)(23,31,33,27)(25,32,34,29)(36,37,41,38)(39,46,47,51)(40,45,50,43)(42,49,44,48);(20,22)(21,25)(23,32)(24,30)(26,34)(27,35)(28,31)(29,33)(36,38,41,37)(39,44,47,42)(40,43,50,45)(46,49,51,48);(23,33)(27,31)(28,35)(29,32)(36,39)(37,42)(38,44)(40,49)(41,47)(43,51)(45,46)(48,50);(21,26)(25,34)(27,31)(28,35)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11995);