C₂²×#595 #63265

order	272
isoclinism	isoclinic class of #595
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³

Aliases

direct product	C₂²×#595
unambiguous semidirect product	D₁₇⋊(C₂×C₄)

Fitting, socle	C₂²×C₁₇ ⋊ C₄
derived, Sylow	C₁₇ ⋊ C₂²×C₄

54 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 3 generators on 21 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(272, 52);