D₇×#41 #6552

order	224
automorphism	Aut(G) = C₂²×S₄×AGL(1,𝔽₇) (order 4032) · Inn(G) = C₂²×D₇ · Out(G) = C₂²×C₃×D₃
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁵

Aliases

Fitting	C₇×#41 ⋊ C₂
Sylow	C₇ ⋊ C₂×#41

164 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 4 generators on 15 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(224, 184);