C₇×Dic₁₈ #92603

order	504
isoclinism	isoclinic class of Dic₁₈
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×Dic₁₈
unambiguous semidirect product	C₉⋊(C₇×Q₈)

Hall	C₇×C₉ ⋊ Q₈
Sylow	C₉ ⋊ C₇×Q₈

36 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 504

A minimal faithful permutation representation — 2 generators on 24 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(504, 29);