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×#18290 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
1034 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)(21,26)(22,30)(23,33)(27,39)(28,37)(29,34)(31,45)(32,44)(35,48)(38,40)(41,51)(42,49)(43,47)(46,50);(20,21)(22,27)(23,34)(24,29)(25,28)(26,33)(30,40)(31,46)(32,41)(35,49)(36,42)(37,48)(38,47)(39,45)(43,51)(44,50);(23,35)(26,37)(31,43)(33,48)(34,49)(38,39)(45,47)(46,51);(20,22,24,32)(21,27,29,41)(23,31,33,47)(25,30,36,44)(26,38,34,46)(28,40,42,50)(35,43,48,45)(37,39,49,51)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11278);