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×#23535 |
| 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 | |
1352 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)(22,31)(23,36)(24,41)(25,29)(26,30)(27,33)(28,39)(32,42)(34,44)(35,43)(37,45)(38,49)(40,46)(47,50)(48,51);(20,22)(21,27)(23,37)(24,34)(25,33)(26,35)(28,45)(29,43)(30,44)(31,41)(32,40)(36,42)(38,48)(39,47)(46,51)(49,50);(20,23,24,39,26,38,25,40)(21,28,29,36,30,46,41,49)(22,32,33,48,35,47,34,37)(27,42,31,45,44,50,43,51);(23,38)(28,46)(32,47)(36,49)(37,48)(39,40)(42,50)(45,51)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16523);