C₈×C₄²⋊C₃ #68020

order	384
isoclinism	isoclinic class of C₄²⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₃×C₈ · Schur multiplier (H₂) = C₄

Aliases

direct product	C₈×C₄²⋊C₃
unambiguous semidirect product	(C₄²×C₈)⋊C₃

Fitting, Sylow	C₄²×C₈ ⋊ C₃
derived	C₄² ⋊ C₃×C₈

88 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 24

A minimal faithful permutation representation — 2 generators on 20 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 596);