Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18316 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24×C4 |
| direct product | C19×#18334 |
| 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 | |
972 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)(22,32)(23,36)(24,33)(28,42)(29,46)(30,39)(31,44)(34,38)(35,37)(40,49)(43,45)(47,50)(48,51);(20,21)(22,28)(23,29)(24,39)(25,31)(26,30)(27,33)(32,43)(34,47)(35,46)(36,45)(37,50)(38,42)(40,51)(41,48)(44,49);(20,22,26,35)(21,28,30,46)(23,33,38,24)(25,32,41,37)(27,42,39,29)(31,43,48,50)(34,49,36,40)(44,45,51,47);(20,23,25,34)(21,29,31,47)(22,33,32,49)(24,37,40,35)(26,38,41,36)(27,43,44,28)(30,42,48,45)(39,50,51,46)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11322);