C₂×D₄×D₇ #6546

order	224
automorphism	Aut(G) = AGL(1,𝔽₇)×#23900 (order 10752) · Inn(G) = C₂²×D₇ · Out(G) = C₃×D₄²
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁶

Aliases

C₂×D₄×D₇

Fitting	C₂×C₇×D₄ ⋊ C₂
Sylow	C₇ ⋊ C₂²×D₄

236 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 4 generators on 13 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(224, 178);