Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18346 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24×C4 |
| direct product | C19×#18370 |
| 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 ◁ C2×C42×C19 ◁ G | |
1024 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)(21,27)(22,24)(23,35)(28,44)(29,42)(30,39)(31,43)(33,48)(34,40)(36,51)(37,50)(38,47)(41,46)(45,49);(20,21)(22,27)(23,36)(24,39)(25,30)(26,31)(28,38)(29,32)(33,49)(34,43)(35,45)(37,41)(40,42)(44,48)(46,47)(50,51);(20,22,32,40)(21,27,29,42)(23,33,47,48)(24,26,34,25)(28,41,45,51)(30,39,31,43)(35,50,38,37)(36,49,46,44);(20,23,32,47)(21,28,29,45)(22,33,40,48)(24,37,34,50)(25,38,26,35)(27,41,42,51)(30,36,31,46)(39,49,43,44)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11358);