Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23998 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#24000 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2404 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#3019 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
1170 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)(22,26)(23,33)(24,37)(25,29)(27,36)(28,39)(30,45)(31,47)(32,42)(34,50)(35,44)(38,43)(40,46)(41,49)(48,51);(20,22,25,32)(21,26,29,42)(23,34)(24,31,39,49)(27,40)(28,41,37,47)(30,35)(33,45)(36,48)(38,46)(43,51)(44,50);(20,23)(21,27)(22,30)(24,38)(25,35)(26,40)(28,44)(29,43)(31,48)(32,34)(33,37)(36,39)(41,50)(42,51)(45,47)(46,49);(24,39)(28,37)(31,49)(33,44)(36,38)(41,47)(45,50)(46,48)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16988);