Finite Group DatabasebetaFinite Group Databasebeta| order | 35340 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic8835 |
| unambiguous semidirect product | C3⋊Dic2945 |
| unambiguous semidirect product | C19⋊Dic465 |
| unambiguous semidirect product | C31⋊Dic285 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D8835 |
| commutator, hypocenter | C3×C5×C19×C31 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C3×C5×C19×C31 | C2 |
| LCS | G ▷ C3×C5×C19×C31 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 62 |
| transitive degree | μt(G) = 35340 |
A minimal faithful permutation representation — 2 generators on 62 points:
(1,2)(3,4)(5,6,7)(8,9,10,11,12)(13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31)(32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62);(1,3,2,4)(6,7)(9,12)(10,11)(14,31)(15,30)(16,29)(17,28)(18,27)(19,26)(20,25)(21,24)(22,23)(33,62)(34,61)(35,60)(36,59)(37,58)(38,57)(39,56)(40,55)(41,54)(42,53)(43,52)(44,51)(45,50)(46,49)(47,48)Polycyclic presentation:
2,3,5,19,31,2|a^2=f,b^a=b^2,c^a=c^4,d^a=d^18,e^a=e^308838 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35340, 25);