Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C22×C4 |
| direct product | C19×#29119 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C2×C19×#117 ◁ G | |
842 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)(22,26)(23,25)(24,27)(28,29,31,33)(30,32,34,35)(36,37,40,45,41,46,39,44)(38,42,47,50,48,51,49,43);(20,22,23,27)(21,24,25,26)(28,30,31,34)(29,32,33,35)(36,38)(37,42)(39,49)(40,47)(41,48)(43,44)(45,50)(46,51);(30,34)(32,35)(36,38)(37,43)(39,47)(40,49)(41,48)(42,44)(45,51)(46,50);(21,25)(24,26)(36,39,41,40)(37,44,46,45)(38,47,48,49)(42,50,51,43)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 22107);