Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| automorphism | Aut(G) = C2×D4×GO+(4,𝔽2) (order 1152) · Inn(G) = D32⋊C4 · Out(G) = C23 |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C32 ⋊ #102 |
88 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)(7,8,10,13,11,14,9,12);(1,2)(3,6)(4,5)(8,12)(9,10)(13,14)Polycyclic presentation:
2^5,3^2|b^2=d,c^2=e,d^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 | #10593284, #10593285, #10593286, … |
| maximal normal subgroup of | #10593284, #10593285, #10593286, … |
| maximal quotient of | #10590016, #10590017, #10590018, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 377);