C₄×#595 #63244

order	272
isoclinism	isoclinic class of #595
automorphism	Aut(G) = D₄×AGL(1,𝔽₁₇) (order 2176) · Inn(G) = #595 · Out(G) = C₄×D₄
homology	Abelianization (H₁) = C₄² · Schur multiplier (H₂) = C₄

Aliases

Fitting	C₄×C₁₇ ⋊ C₄
derived, Sylow	C₁₇ ⋊ C₄²

30 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 68

A minimal faithful permutation representation — 2 generators on 21 points:

(2,3,4,6)(5,8,9,13)(7,12,10,11)(14,16,17,15);(1,2,5,10,6,11,15,17,13,8,14,16,12,3,7,9,4)(18,19,20,21)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(272, 31);