Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18376 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24×C4 |
| direct product | C19×#18400 |
| 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 | |
978 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)(21,28)(22,33)(23,35)(24,38)(29,44)(30,46)(31,39)(32,45)(34,37)(36,49)(40,41)(42,51)(43,47)(48,50);(20,21)(22,29)(23,36)(24,39)(25,42)(26,31)(27,32)(28,38)(30,33)(34,49)(35,47)(37,44)(40,45)(41,51)(43,48)(46,50);(20,22,27,23)(21,29,32,36)(24,37,41,34)(25,33,26,35)(28,43,45,46)(30,31,47,42)(38,48,40,50)(39,44,51,49);(20,23,27,22)(21,30,32,47)(24,37,41,34)(25,35,26,33)(28,44,45,49)(29,31,36,42)(38,48,40,50)(39,43,51,46)817 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11388);