D₇×C₃₂ #89241

order	448
isoclinism	isoclinic class of D₇
automorphism	Aut(G) = C₂²×C₈×AGL(1,𝔽₇) (order 1344) · Inn(G) = D₇ · Out(G) = C₂²×C₃×C₈
homology	Abelianization (H₁) = C₂×C₃₂ · Schur multiplier (H₂) = C₂

Aliases

D₇×C₃₂

Fitting	C₇×C₃₂ ⋊ C₂
derived, Sylow	C₇ ⋊ C₂×C₃₂

34 conjugacy classes of subgroups.

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 224

A minimal faithful permutation representation — 2 generators on 39 points:

(2,3)(4,5)(6,7);(1,2,4,6,7,5,3)(8,9,10,14,11,15,18,24,12,16,19,25,21,27,30,34,13,17,20,26,22,28,31,35,23,29,32,36,33,37,38,39)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(448, 3);