C₂×#338⋊C₃ #68022

order	384
isoclinism	isoclinic class of #338⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂×#338⋊C₃
unambiguous semidirect product	(C₂×#338)⋊C₃

Fitting, Sylow	C₂×#338 ⋊ C₃
derived	#338 ⋊ C₂×C₃

	subgroup	G/H
center, hypercenter	C₂×C₄	C₄²⋊C₃
commutator, cosocle, hypocenter	#338	C₂×C₃
Frattini	C₂²×C₄	C₂×A₄
Fitting	C₂×#338	C₃
socle	C₂²	#95⋊C₃
LCS	G ▷ #338
UCS	C₁ ◁ C₂×C₄

92 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 32

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 598);