C₃×D₆₃ #67383

order	378
isoclinism	isoclinic class of D₆₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

C₃×D₆₃

	subgroup	G/H
center, hypercenter	C₃	D₆₃
commutator, cosocle, hypocenter	C₇×C₉	C₂×C₃
Frattini	C₃	C₃×D₂₁
Fitting	C₃×C₇×C₉	C₂
socle	C₃²×C₇	D₃
LCS	G ▷ C₇×C₉
UCS	C₁ ◁ C₃

28 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 126

A minimal faithful permutation representation — 2 generators on 19 points:

(1,2,3)(5,6)(7,8)(9,10)(12,14)(13,17)(15,16)(18,19);(4,5,7,9,10,8,6)(11,19,14,17,16,15,13,12,18)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(378, 36);