D₇×C₃⋊Dic₃ #92673

order	504
isoclinism	isoclinic class of D₇×C₃⋊D₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	D₇×C₃⋊Dic₃
unambiguous semidirect product	(C₃×D₇)⋊Dic₃

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₇×C₃⋊D₃
commutator, hypocenter	C₃²×C₇	C₂×C₄
Fitting, socle, cosocle	C₂×C₃²×C₇	C₂²
prime radical	C₂×C₃²×D₇	C₂
LCS	G ▷ C₃²×C₇
UCS	C₁ ◁ C₂

96 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 252

A minimal faithful permutation representation — 3 generators on 17 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(504, 99);