Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#19029 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C19×#121 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
824 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 2432 |
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)(20,21,25,23)(22,28,30,35)(24,32,34,27)(26,33,29,31)(38,44)(39,46)(41,49)(42,47)(45,48)(50,51);(20,22,25,30)(21,26,23,29)(24,33,34,31)(27,35,32,28)(36,37,40,43)(38,41,45,50)(39,47,46,42)(44,51,48,49);(20,23,25,21)(22,29,30,26)(24,27,34,32)(28,33,35,31)(36,38)(37,41)(39,48)(40,45)(42,51)(43,50)(44,46)(47,49);(22,30)(26,29)(28,35)(31,33)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 12017);