D₇×D₈ #6473

order	224
automorphism	Aut(G) = C₂×AGL(1,ℤ/8)×AGL(1,𝔽₇) (order 2688) · Inn(G) = D₄×D₇ · Out(G) = C₂³×C₃
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

D₇×D₈

Fitting	C₇×D₈ ⋊ C₂
Sylow	C₇ ⋊ C₂×D₈

76 conjugacy classes of subgroups.

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 56

A minimal faithful permutation representation — 3 generators on 15 points:

(2,5)(3,8)(6,7)(9,10,12,14,15,13,11);(1,2)(3,5)(4,7)(6,8);(10,11)(12,13)(14,15)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(224, 105);