C₇×Dic₁₂ #66609

order	336
isoclinism	isoclinic class of #204
automorphism	Aut(G) = C₂×C₃×D₃×AGL(1,ℤ/8) (order 1152) · Inn(G) = D₁₂ · Out(G) = C₂⁴×C₃
homology	Abelianization (H₁) = C₂²×C₇ · Schur multiplier (H₂) = C₁

Aliases

C₇×Dic₁₂

Hall	C₃×C₇ ⋊ Q₁₆
Sylow	C₃ ⋊ C₇×Q₁₆

36 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 336

A minimal faithful permutation representation — 2 generators on 26 points:

(1,2,3,4,5,6,7)(8,9,10,11,12,13,14,15)(16,23,22,21,20,19,18,17)(24,25,26);(8,16,12,20)(9,17,13,21)(10,18,14,22)(11,19,15,23)(25,26)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(336, 78);