Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33551 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#33554 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | C2×B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×D4 | C24×C19 |
| prime radical | C19×#3025 | C2 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C2×C4×C19 ◁ C2×#41×C19 ◁ G | |
1112 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)(23,27)(24,28)(25,29)(26,32)(31,44)(33,45)(34,48)(35,41)(36,42)(37,43)(38,46)(39,47)(40,49)(50,51);(20,22,25,33)(21,26,29,39)(23,34,36,31)(24,32,37,47)(27,40,42,38)(28,30,43,45)(35,49,50,46)(41,48,51,44);(24,37)(32,47)(35,50)(46,49);(20,23,25,36)(21,27,29,42)(22,31,33,34)(24,35,37,50)(26,38,39,40)(28,41,43,51)(30,44,45,48)(32,46,47,49)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26542);