C₈×D₇ #1130

order	112
isoclinism	isoclinic class of D₇
automorphism	Aut(G) = C₂³×AGL(1,𝔽₇) (order 336) · Inn(G) = D₇ · Out(G) = C₂³×C₃
homology	Abelianization (H₁) = C₂×C₈ · Schur multiplier (H₂) = C₂

Aliases

C₈×D₇

Fitting	C₇×C₈ ⋊ C₂
derived, Sylow	C₇ ⋊ C₂×C₈

22 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 2 generators on 15 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(112, 3);