Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| automorphism | Aut(G) = C2×#64241 (order 576) · Inn(G) = D32⋊C4 · Out(G) = C22 |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C32 ⋊ #104 |
79 conjugacy classes of subgroups.
| minimal degree | μ(G) = 14 |
| transitive degree | μt(G) = 24 |
A minimal faithful permutation representation — 2 generators on 14 points:
(1,3)(2,5,6)(8,11,13,12);(1,2)(3,6)(4,5)(7,8)(9,11)(10,13)(12,14)Polycyclic presentation:
2^5,3^2|b^2=d,c^2=e,b^a=bc,c^a=ce,d^a=de,f^a=f^2,f^b=g,g^b=f,f^c=f^2,g^c=g^227 conjugacy classes — view the full character table.
| maximal subgroup of | #10593380, #10593381, #10593451, … |
| maximal normal subgroup of | #10593380, #10593381, #10593451, … |
| maximal quotient of | #10590030, #10590031, #10590035, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 389);