Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23472 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#23527 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | C2×#124 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C2×C19 | C2×#394 |
| prime radical | C2×C19×#575 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C23×C4×C19 ◁ G | |
1336 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
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)(22,30)(23,34)(24,38)(25,29)(26,32)(27,36)(28,40)(31,45)(33,44)(35,49)(37,43)(39,42)(41,46)(47,50)(48,51);(20,22)(21,26)(23,35)(24,39)(25,33)(27,41)(28,44)(29,42)(30,38)(31,36)(32,40)(34,47)(37,46)(43,49)(45,48)(50,51);(20,23,24,37,25,36,40,51)(21,27,28,43,29,34,38,48)(22,31,32,46,33,35,39,50)(26,41,30,45,42,47,44,49);(23,36)(27,34)(31,35)(37,51)(41,47)(43,48)(45,49)(46,50)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16515);