Finite Group DatabasebetaFinite Group Databasebeta| order | 936 |
| automorphism | Aut(G) order 67392 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
| dicyclic | Dic234 |
| Hall | C9×C13 ⋊ Q8 |
| Sylow | C13 ⋊ Dic18 |
| Sylow | C9 ⋊ Dic26 |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 30 |
| transitive degree | μt(G) = 936 |
A minimal faithful permutation representation — 2 generators on 30 points:
(1,2,3,4)(5,8,7,6)(9,10,11,12,13,14,15,16,17)(18,19,20,21,22,23,24,25,26,27,28,29,30);(1,5,3,7)(2,6,4,8)(10,17)(11,16)(12,15)(13,14)(19,30)(20,29)(21,28)(22,27)(23,26)(24,25)Polycyclic presentation:
2^3,3,13,3|a^2=c,b^2=c,d^3=f,b^a=bc,d^a=d^2f^2,e^a=e^12,f^a=f^2237 conjugacy classes — view the full character table.
| maximal subgroup of | #14272402, #14272405, #14272411, … |
| maximal normal subgroup of | #14272402, #14272405, #14272411, … |
| maximal quotient of | #14272473, C4⋊Dic117, C2×Dic234, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(936, 37);