Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18247 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#121 | C23 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
852 conjugacy classes of subgroups.
| minimal degree | μ(G) = 67 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 generators on 67 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(25,31)(32,35)(36,37,41,45)(38,46,49,59)(39,43,50,57)(40,52,54,44)(42,53,56,48)(47,60,61,67)(51,64,63,58)(55,65,66,62);(20,21)(22,25)(23,26)(24,27)(28,32)(29,31)(30,33)(34,35)(36,38,41,49)(37,42,45,56)(39,47,50,61)(40,53,54,48)(43,55,57,66)(44,59,52,46)(51,65,63,62)(58,67,64,60);(20,22)(21,25)(23,28)(24,29)(26,32)(27,31)(30,34)(33,35)(36,39,41,50)(37,43,45,57)(38,47,49,61)(40,51,54,63)(42,55,56,66)(44,58,52,64)(46,60,59,67)(48,62,53,65);(20,23,24,30)(21,26,27,33)(22,28,29,34)(25,32,31,35)(39,50)(43,57)(47,61)(51,63)(55,66)(58,64)(60,67)(62,65)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11235);