C₂×C₇×Dic₉ #92606

order	504
isoclinism	isoclinic class of D₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₇×Dic₉
unambiguous semidirect product	(C₂×C₉)⋊(C₄×C₇)

derived, Sylow	C₉ ⋊ C₂×C₄×C₇
Hall	C₇×C₉ ⋊ C₂×C₄

48 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 504

A minimal faithful permutation representation — 2 generators on 22 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(504, 32);