Finite Group DatabasebetaFinite Group Databasebeta| order | 912 |
| automorphism | Aut(G) order 65664 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
| dicyclic | Dic228 |
| Hall | C3×C19 ⋊ Q16 |
| Sylow | C19 ⋊ Dic12 |
| Sylow | C3 ⋊ Dic76 |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 38 |
| transitive degree | μt(G) = 912 |
A minimal faithful permutation representation — 2 generators on 38 points:
(1,2,3,4,5,6,7,8)(9,16,15,14,13,12,11,10)(17,18,19)(20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38);(1,9,5,13)(2,10,6,14)(3,11,7,15)(4,12,8,16)(18,19)(21,38)(22,37)(23,36)(24,35)(25,34)(26,33)(27,32)(28,31)(29,30)Polycyclic presentation:
2^4,3,19|a^2=d,b^2=cd,c^2=d,b^a=bc,c^a=cd,e^a=e^2,f^a=f^18231 conjugacy classes — view the full character table.
| maximal subgroup of | #14268832, #14268834, #14268837, … |
| maximal normal subgroup of | #14268832, #14268834, #14268837, … |
| maximal quotient of | #14269011, #14269015, C2×Dic228, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(912, 94);