D₃×C₇² #64431

order	294
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₇² · Schur multiplier (H₂) = C₇

Aliases

direct product	D₃×C₇²
unambiguous semidirect product	C₃⋊(C₂×C₇²)

Fitting, socle, Hall	C₃×C₇² ⋊ C₂
derived, Sylow	C₃ ⋊ C₂×C₇²

	subgroup	G/H
center, hypercenter	C₇²	D₃
commutator, cosocle, hypocenter	C₃	C₂×C₇²
Frattini	C₁	G
Fitting, socle	C₃×C₇²	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₇²

40 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 147

A minimal faithful permutation representation — 2 generators on 17 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(294, 20);