C₂³×#261 #88266

order	416
isoclinism	isoclinic class of #261
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product	C₂³×#261
unambiguous semidirect product	D₁₃⋊(C₂²×C₄)

Fitting, socle	C₂³×C₁₃ ⋊ C₄
derived, Sylow	C₁₃ ⋊ C₂³×C₄

236 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 4 generators on 19 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(416, 233);