C₇⋊#95 #6405

order	224
isoclinism	isoclinic class of Dic₁₄
automorphism	Aut(G) = AGL(1,𝔽₇)×#2846 (order 5376) · Inn(G) = C₂×D₇ · Out(G) = C₂×C₃×#120
homology	Abelianization (H₁) = C₄² · Schur multiplier (H₂) = C₂³

Aliases

C₇ ⋊ #95

76 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 224

A minimal faithful permutation representation — 2 generators on 19 points:

(1,2,4,6,7,5,3)(12,13,14,15)(17,19);(2,3)(4,5)(6,7)(8,9,10,11)(16,17)(18,19)

Polycyclic presentation:

2^5,7|a^2=c,b^2=d,b^a=be,f^a=f^6

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(224, 37);