D₃²×C₈ #63789

order	288
isoclinism	isoclinic class of D₃²
automorphism	Aut(G) = C₂²×#64241 (order 1152) · Inn(G) = D₃² · Out(G) = C₂²×D₄
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂³

Aliases

D₃²×C₈

Fitting	C₃²×C₈ ⋊ C₂²
derived, Sylow	C₃² ⋊ C₂²×C₈

163 conjugacy classes of subgroups.

minimal degree	μ(G) = 14
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 3 generators on 14 points:

(9,10,11)(13,14);(10,11)(12,13,14);(1,2,3,5,4,6,7,8)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 437);