order	112
isoclinism	isoclinic class of Dic₁₄
automorphism	Aut(G) = AGL(1,𝔽₇)×B(4,𝔽₂) (order 2688) · Inn(G) = C₂×D₇ · Out(G) = C₃×#120
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

C₂×D₂₈

Splittings

Fitting	C₂×C₄×C₇ ⋊ C₂
Sylow	C₇ ⋊ C₂×D₄

54 conjugacy classes of subgroups.

minimal degree	μ(G) = 13
transitive degree	μ_t(G) = 56

A minimal faithful permutation representation — 3 generators on 13 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(112, 29);