Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#23717 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | #121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C22×C19 | C2×#121 |
| prime radical | C2×#41×C19 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C2×C42×C19 ◁ G | |
752 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,25)(23,24)(26,27)(28,29,32,37,34,39,33,38)(30,35,41,50,42,51,48,55)(31,43,45,54,47,53,46,36)(40,52,44,58,56,59,57,49);(21,24)(25,27)(28,30)(29,35)(31,44)(32,41)(33,48)(34,42)(36,52)(37,50)(38,55)(39,51)(40,46)(43,58)(45,56)(47,57)(49,53)(54,59);(28,31,34,47)(29,36,39,54)(30,40,42,56)(32,46,33,45)(35,49,51,58)(37,53,38,43)(41,57,48,44)(50,59,55,52);(20,22,23,26)(21,25,24,27)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16705);