Finite Group DatabasebetaFinite Group Databasebeta| order | 31668 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic7917 |
| unambiguous semidirect product | C3⋊Dic2639 |
| unambiguous semidirect product | C7⋊Dic1131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D7917 |
| commutator, hypocenter | C3×C7×C13×C29 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C3×C7×C13×C29 | C2 |
| LCS | G ▷ C3×C7×C13×C29 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 56 |
| transitive degree | μt(G) = 31668 |
A minimal faithful permutation representation — 2 generators on 56 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);(1,3,2,4)(6,7)(9,14)(10,13)(11,12)(16,27)(17,26)(18,25)(19,24)(20,23)(21,22)(29,56)(30,55)(31,54)(32,53)(33,52)(34,51)(35,50)(36,49)(37,48)(38,47)(39,46)(40,45)(41,44)(42,43)Polycyclic presentation:
2,3,7,13,29,2|a^2=f,b^a=b^2,c^a=c^6,d^a=d^12,e^a=e^287920 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic15834 |
| maximal normal subgroup of | Dic15834 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31668, 22);