Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24420 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#24422 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2410 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
1300 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)(20,21,26,30,25,23,27,31)(22,28,35,43,34,37,36,32)(24,29,40,44,39,38,41,45)(33,42,48,46,47,50,49,51);(20,22,25,34)(21,28,23,37)(24,33,39,47)(26,36,27,35)(29,42,38,50)(30,32,31,43)(40,49,41,48)(44,51,45,46);(20,23)(21,25)(22,32)(24,38)(26,30)(27,31)(28,36)(29,39)(33,46)(34,43)(35,37)(40,44)(41,45)(42,48)(47,51)(49,50);(20,24)(21,29)(22,33)(23,38)(25,39)(26,41)(27,40)(28,42)(30,45)(31,44)(32,46)(34,47)(35,49)(36,48)(37,50)(43,51)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 17410);