Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23439 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#23532 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
1326 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 generators on 55 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,23)(24,25)(26,36)(27,41)(28,34)(29,33)(30,35)(31,38)(32,45)(37,46)(39,48)(40,47)(42,54)(43,50)(44,49)(51,53)(52,55);(24,26,30,40)(25,31,35,48)(27,42,43,37)(28,39,29,38)(32,46,49,54)(33,47,34,36)(41,51,50,55)(44,52,45,53);(21,23)(24,27,28,44,30,43,29,45)(25,32,33,50,35,49,34,41)(26,37,38,52,40,42,39,53)(31,46,36,51,48,54,47,55);(27,43)(32,49)(37,42)(41,50)(44,45)(46,54)(51,55)(52,53)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16520);