C₂×C₂²⋊#261 #88244

order	416
isoclinism	isoclinic class of #6118
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product	C₂×C₂²⋊#261
unambiguous semidirect product	D₁₃⋊(C₂²⋊C₄)
unambiguous semidirect product	(C₂×#261)⋊C₂²

Fitting	C₂³×C₁₃ ⋊ C₄
Sylow	C₁₃ ⋊ C₂×C₂²⋊C₄

132 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 104

A minimal faithful permutation representation — 3 generators on 19 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(416, 211);