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) = C33×C9 |
| direct product | C3×C19×#6898 |
| 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 | |
692 conjugacy classes of subgroups.
| minimal degree | μ(G) = 76 |
| transitive degree | μt(G) = 4617 |
A minimal faithful permutation representation — 4 generators on 76 points:
(1,2,3)(58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76);(4,5,8)(6,10,16)(7,11,15)(9,17,14)(12,19,24)(13,20,23)(18,25,22)(21,27,29)(26,30,28)(31,32,35)(33,36,42)(34,38,43)(37,47,41)(39,44,50)(40,46,51)(45,54,49)(48,53,56)(52,57,55);(5,9,11)(8,15,17)(10,18,20)(16,23,25)(19,26,27)(24,29,30)(31,33,39,34,40,48,41,49,55)(32,36,44,38,46,53,37,45,52)(35,42,50,43,51,56,47,54,57);(4,6,12,14,22,28,7,13,21)(5,10,19,9,18,26,11,20,27)(8,16,24,17,25,30,15,23,29)(32,37,38)(35,43,47)(36,45,46)(42,51,54)(44,52,53)(50,56,57)2907 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13851, 435);