Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24292 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#26852 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C2×#41×C19 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C22×C4×C19 ◁ G | |
698 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,27)(23,25)(24,26)(28,29)(30,41)(31,47)(32,51)(33,39)(34,40)(35,44)(36,49)(37,42)(38,52)(43,55)(45,54)(46,56)(48,57)(50,58)(53,59);(20,22,24,23)(21,25,26,27)(28,30,33,44,34,46,52,45)(29,35,38,41,40,54,39,56)(31,48,49,59,50,32,43,42)(36,51,47,53,55,57,58,37);(20,23,24,22)(21,25,26,27)(28,31,33,49,34,50,52,43)(29,36,38,47,40,55,39,58)(30,42,44,48,46,59,45,32)(35,53,41,57,54,37,56,51);(21,26)(25,27)(28,32,33,42,34,48,52,59)(29,37,38,51,40,53,39,57)(30,43,44,31,46,49,45,50)(35,36,41,47,54,55,56,58)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 19840);