Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33539 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#33539 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | C2×#447 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ C2×C19×#131 ◁ G | |
1130 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)(22,33)(23,37)(24,32)(25,31)(26,29)(27,34)(28,35)(30,40)(36,48)(38,49)(39,43)(41,47)(42,46)(44,50)(45,51);(20,22)(21,27)(23,38)(24,35)(25,42)(26,36)(28,43)(29,44)(30,46)(31,45)(32,49)(33,37)(34,40)(39,50)(41,51)(47,48);(20,22)(21,28)(23,34)(24,42)(25,35)(26,36)(27,43)(29,46)(30,44)(31,48)(32,33)(37,49)(38,40)(39,51)(41,50)(45,47);(21,29)(27,44)(28,46)(30,43)(31,32)(33,48)(37,47)(45,49)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26527);