Finite Group DatabasebetaFinite Group Databasebeta| order | 4617 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of C32⋊H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C19 · Schur multiplier (H2) = C3 |
| direct product | C19×#6899 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C32×C19 | C33 |
| commutator, Frattini, cosocle | C32 | C33×C19 |
| prime radical | C33×C19 | C32 |
| LCS | G ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C32×C19 ◁ G | |
110 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 1539 |
A minimal faithful permutation representation — 3 generators on 55 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,24,22)(25,26,27)(29,30,34)(31,38,50)(32,36,44)(33,37,45)(35,46,41)(39,49,53)(40,51,43)(42,48,54)(47,55,52);(20,21,25,28,22,26,23,24,27)(29,31,39,33,40,52,42,41,32)(30,35,47,37,38,36,48,51,49)(34,43,44,45,46,53,54,50,55);(20,22,27,28,24,25,23,21,26)(29,32,41,42,52,40,33,39,31)(30,36,35,48,47,51,37,49,38)(34,44,46,54,55,43,45,53,50)969 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4617, 46);