Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18284 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18313 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#3455 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
910 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)(20,21,25,28)(22,29,31,34)(23,27,24,32)(26,33,35,30)(37,42)(39,40)(43,50)(44,47)(45,48)(49,51);(20,22)(21,26)(23,30)(24,33)(25,31)(27,34)(28,35)(29,32)(36,37)(38,43)(39,42)(40,47)(41,44)(45,49)(46,51)(48,50);(20,23,25,24)(21,27,28,32)(22,30,31,33)(26,34,35,29)(36,38,41,46)(37,43,44,51)(39,45,40,48)(42,49,47,50);(36,39,41,40)(37,42,44,47)(38,45,46,48)(43,49,51,50)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11301);