Finite Group DatabasebetaFinite Group Databasebeta| order | 13851 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of C32⋊H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C34×C19 · Schur multiplier (H2) = C34 |
| direct product | C3×C19×#6899 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C33×C19 | C33 |
| commutator, Frattini, cosocle | C32 | C34×C19 |
| prime radical | C34×C19 | C32 |
| LCS | G ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C33×C19 ◁ G | |
788 conjugacy classes of subgroups.
| minimal degree | μ(G) = 58 |
| transitive degree | μt(G) = 4617 |
A minimal faithful permutation representation — 4 generators on 58 points:
(1,2,3)(40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58);(5,8,6)(9,10,11)(13,14,18)(15,22,34)(16,20,28)(17,21,29)(19,30,25)(23,33,37)(24,35,27)(26,32,38)(31,39,36);(4,5,9,12,6,10,7,8,11)(13,15,23,17,24,36,26,25,16)(14,19,31,21,22,20,32,35,33)(18,27,28,29,30,37,38,34,39);(4,6,11,12,8,9,7,5,10)(13,16,25,26,36,24,17,23,15)(14,20,19,32,31,35,21,33,22)(18,28,30,38,39,27,29,37,34)2907 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13851, 436);