Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23886 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#24462 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C2×C19×#578 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C22×C4×C19 ◁ G | |
1302 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)(24,25,30,34)(26,36,39,46)(27,40,44,32)(28,38,31,47)(29,35,48,33)(37,53,55,50)(41,49,54,42)(43,51,45,52);(24,26,30,39)(25,31,34,28)(27,41,44,54)(29,47,48,38)(32,50,40,53)(33,46,35,36)(37,43,55,45)(42,51,49,52);(21,23)(24,27,30,44)(25,32,34,40)(26,37,39,55)(28,42,31,49)(29,43,48,45)(33,51,35,52)(36,50,46,53)(38,54,47,41);(24,28)(25,26)(27,42)(29,36)(30,31)(32,37)(33,47)(34,39)(35,38)(40,55)(41,51)(43,50)(44,49)(45,53)(46,48)(52,54)817 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 17450);