Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18252 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18283 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#538 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
886 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1216 |
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)(25,31)(32,35)(36,37,40,42)(38,44,46,51)(39,47,49,43)(41,48,50,45);(20,21)(22,25)(23,26)(24,27)(28,32)(29,31)(30,33)(34,35)(36,38,40,46)(37,41,42,50)(39,48,49,45)(43,51,47,44);(20,22)(21,25)(23,28)(24,29)(26,32)(27,31)(30,34)(33,35)(36,37)(38,41)(39,47)(40,42)(43,49)(44,48)(45,51)(46,50);(20,23,24,30)(21,26,27,33)(22,28,29,34)(25,32,31,35)(37,42)(41,50)(43,47)(44,51)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11271);