Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#33347 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | C2×#99 |
| commutator | C23 | C23×C4×C19 |
| Frattini, cosocle | C2×D4 | C24×C19 |
| socle | C2×C19 | C22×#99 |
| prime radical | C19×#3449 | C2 |
| LCS | G ▷ C23 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C22×C4×C19 ◁ C22×#41×C19 ◁ G | |
1236 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)(24,36,37,28)(25,29)(26,33,38,45)(31,42)(32,43)(34,47,48,40)(35,41)(39,46,49,51)(44,50);(20,22)(21,26)(23,32)(24,33)(25,31)(27,39)(28,30)(29,38)(34,46)(35,44)(36,42)(37,45)(40,43)(41,49)(47,50)(48,51);(22,31)(26,38)(30,42)(32,44)(33,45)(39,49)(43,50)(46,51);(20,23,25,35)(21,27,29,41)(22,32,31,44)(24,34,37,48)(26,39,38,49)(28,40,36,47)(30,43,42,50)(33,46,45,51)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26335);