C₂⁶×D₃ #87592

order	384
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₂⁷ · Schur multiplier (H₂) = C₂²¹

Aliases

C₂⁶×D₃

Fitting, socle	C₂⁶×C₃ ⋊ C₂
derived, Sylow	C₃ ⋊ C₂⁷

	subgroup	G/H
center, hypercenter	C₂⁶	D₃
commutator, cosocle, hypocenter	C₃	C₂⁷
Frattini	C₁	G
Fitting, socle	C₂⁶×C₃	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₂⁶

58424 conjugacy classes of subgroups.

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 192

A minimal faithful permutation representation — 7 generators on 15 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 20168);