Finite Group DatabasebetaFinite Group Databasebeta| order | 30940 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic7735 |
| unambiguous semidirect product | C7⋊Dic1105 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D7735 |
| commutator, hypocenter | C5×C7×C13×C17 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C5×C7×C13×C17 | C2 |
| LCS | G ▷ C5×C7×C13×C17 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 46 |
| transitive degree | μt(G) = 30940 |
A minimal faithful permutation representation — 2 generators on 46 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);(1,3,2,4)(6,9)(7,8)(11,16)(12,15)(13,14)(18,29)(19,28)(20,27)(21,26)(22,25)(23,24)(31,46)(32,45)(33,44)(34,43)(35,42)(36,41)(37,40)(38,39)Polycyclic presentation:
2,5,7,13,17,2|a^2=f,b^a=b^4,c^a=c^6,d^a=d^12,e^a=e^167738 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic15470 |
| maximal normal subgroup of | Dic15470 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30940, 16);