Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18284 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18287 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C25×C19 | D4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
1064 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)(20,21,24,29)(22,30,33,43)(23,34,37,28)(25,27,38,42)(26,35,40,31)(32,44,46,51)(36,47,49,41)(39,48,50,45);(20,22,24,33)(21,26,29,40)(23,35,37,31)(25,32,38,46)(27,39,42,50)(28,43,34,30)(36,48,49,45)(41,51,47,44);(23,36)(28,41)(30,44)(31,45)(34,47)(35,48)(37,49)(43,51);(21,27)(26,39)(28,41)(29,42)(30,44)(34,47)(40,50)(43,51)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11275);