Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33758 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#33801 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C19×#3169 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ C2×C4×C8×C19 ◁ G | |
500 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 2432 |
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)(22,28)(23,26)(24,27)(25,30)(29,34)(31,33)(32,35)(37,41)(38,44)(40,47)(42,50)(43,46)(45,51)(48,49);(20,22,24,30)(21,25,27,28)(23,31,32,29)(26,34,35,33)(36,37,39,41)(38,42,45,49)(40,43,46,47)(44,48,51,50);(20,23,24,32)(21,26,27,35)(22,29,30,31)(25,33,28,34)(36,38,39,45)(37,42,41,49)(40,48,46,50)(43,51,47,44);(21,27)(25,28)(26,35)(33,34)(36,37,39,41)(38,42,45,49)(40,43,46,47)(44,48,51,50)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26789);