C₃×C₇×D₉ #67379

order	378
isoclinism	isoclinic class of D₉
automorphism	Aut(G) = C₂²×C₃×AGL(1,ℤ/9) (order 648) · Inn(G) = D₉ · Out(G) = C₂²×C₃²
homology	Abelianization (H₁) = C₂×C₃×C₇ · Schur multiplier (H₂) = C₁

Aliases

C₃×C₇×D₉

	subgroup	G/H
center, hypercenter	C₃×C₇	D₉
commutator, cosocle, hypocenter	C₉	C₂×C₃×C₇
Frattini	C₃	C₃×D₃×C₇
Fitting	C₃×C₇×C₉	C₂
socle	C₃²×C₇	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₃×C₇

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(378, 32);