Finite Group DatabasebetaFinite Group Databasebeta| order | 144 |
| isoclinism | isoclinic class of Dic18 |
| automorphism | Aut(G) = C2×D4×AGL(1,ℤ/9) (order 864) · Inn(G) = C2×D9 · Out(G) = C23×C3 |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C9 ⋊ M16 |
30 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 72 |
A minimal faithful permutation representation — 2 generators on 17 points:
(1,6,8,7,2,4,3,9,5)(11,14)(15,17);(2,4)(3,7)(5,6)(8,9)(10,11,12,15,13,14,16,17)Polycyclic presentation:
2^4,3^2|a^2=c,c^2=d,e^3=f^2,b^a=bd,e^a=e^2f,f^a=f^242 conjugacy classes — view the full character table.
| maximal subgroup of | #63364, #63372, #63381, … |
| maximal normal subgroup of | #63364, #63372, #63381, … |
| maximal quotient of | #63362, C4⋊(C9⋊C8), #63389, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(144, 10);