Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33618 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#33618 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | C2×#466 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ C2×C19×#131 ◁ G | |
656 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)(22,33)(23,28)(24,25)(29,44)(30,40)(31,42)(32,41)(34,48)(35,38)(36,37)(39,46)(45,51)(47,50);(20,21,28,42,25,32,37,40,26,30,36,41,24,31,23,27)(22,29,43,44,33,46,48,50,35,45,49,51,38,47,34,39);(20,22)(21,29)(23,34)(24,38)(25,33)(26,35)(27,39)(28,43)(30,45)(31,47)(32,46)(36,49)(37,48)(40,50)(41,51)(42,44);(21,30)(27,40)(29,45)(31,32)(39,50)(41,42)(44,51)(46,47)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26606);