D₃²×D₇ #92746

order	504
isoclinism	isoclinic class of D₃²×D₇
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

direct product	D₃²×D₇
unambiguous semidirect product	(C₃×D₃×D₇)⋊C₂
unambiguous semidirect product	(D₇×C₃⋊D₃)⋊C₂
unambiguous semidirect product	(D₃×D₂₁)⋊C₂

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₇	C₂³
LCS	G ▷ C₃²×C₇
UCS	C₁

138 conjugacy classes of subgroups.

minimal degree	μ(G) = 13
transitive degree	μ_t(G) = 42

A minimal faithful permutation representation — 3 generators on 13 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(504, 172);