Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18446 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24×C4 |
| direct product | C19×#18458 |
| 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 | |
1036 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)(23,34)(27,40)(28,38)(29,35)(31,33)(32,47)(36,49)(39,44)(41,51)(42,48)(43,50)(45,46);(20,21)(22,27)(23,35)(24,29)(25,28)(26,34)(30,44)(31,41)(32,48)(33,42)(36,50)(37,43)(38,49)(39,46)(40,47)(45,51);(22,31)(23,36)(26,38)(27,41)(30,33)(32,45)(34,49)(35,50)(39,40)(42,44)(46,47)(48,51);(20,22,25,33)(21,27,28,42)(23,32,36,47)(24,31,37,30)(26,39,38,51)(29,41,43,44)(34,46,49,45)(35,48,50,40)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11446);