Finite Group DatabasebetaFinite Group Databasebeta| order | 31620 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic7905 |
| unambiguous semidirect product | C3⋊Dic2635 |
| unambiguous semidirect product | C31⋊Dic255 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D7905 |
| commutator, hypocenter | C3×C5×C17×C31 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C3×C5×C17×C31 | C2 |
| LCS | G ▷ C3×C5×C17×C31 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 60 |
| transitive degree | μt(G) = 31620 |
A minimal faithful permutation representation — 2 generators on 60 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);(1,3,2,4)(6,7)(9,12)(10,11)(14,29)(15,28)(16,27)(17,26)(18,25)(19,24)(20,23)(21,22)(31,60)(32,59)(33,58)(34,57)(35,56)(36,55)(37,54)(38,53)(39,52)(40,51)(41,50)(42,49)(43,48)(44,47)(45,46)Polycyclic presentation:
2,3,5,17,31,2|a^2=f,b^a=b^2,c^a=c^4,d^a=d^16,e^a=e^307908 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic15810 |
| maximal normal subgroup of | Dic15810 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31620, 19);