D₇×C₃⋊C₈ #66554

order	336
isoclinism	isoclinic class of D₃×D₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₈ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₇×C₃⋊C₈
unambiguous semidirect product	(C₃×D₇)⋊C₈

	subgroup	G/H
center, Frattini, hypercenter	C₄	D₃×D₇
commutator, hypocenter	C₃×C₇	C₂×C₈
Fitting, cosocle	C₃×C₄×C₇	C₂²
socle	C₂×C₃×C₇	C₂×C₄
prime radical	C₂×C₃×D₇	C₄
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₄

44 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 168

A minimal faithful permutation representation — 2 generators on 18 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(336, 23);