C₃²×Dic₁₄ #92702

order	504
isoclinism	isoclinic class of Dic₁₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃² · Schur multiplier (H₂) = C₃

Aliases

C₃²×Dic₁₄

Hall	C₃²×C₇ ⋊ Q₈
Sylow	C₇ ⋊ C₃²×Q₈

72 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 504

A minimal faithful permutation representation — 2 generators on 21 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(504, 128);