Finite Group DatabasebetaFinite Group Databasebeta| order | 31980 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic7995 |
| unambiguous semidirect product | C3⋊Dic2665 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D7995 |
| commutator, hypocenter | C3×C5×C13×C41 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C3×C5×C13×C41 | C2 |
| LCS | G ▷ C3×C5×C13×C41 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 66 |
| transitive degree | μt(G) = 31980 |
A minimal faithful permutation representation — 2 generators on 66 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)(26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66);(1,3,2,4)(6,7)(9,12)(10,11)(14,25)(15,24)(16,23)(17,22)(18,21)(19,20)(27,66)(28,65)(29,64)(30,63)(31,62)(32,61)(33,60)(34,59)(35,58)(36,57)(37,56)(38,55)(39,54)(40,53)(41,52)(42,51)(43,50)(44,49)(45,48)(46,47)Polycyclic presentation:
2,3,5,13,41,2|a^2=f,b^a=b^2,c^a=c^4,d^a=d^12,e^a=e^407998 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic15990 |
| maximal normal subgroup of | Dic15990 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31980, 19);