C₃²×D₂₁ #67402

order	378
isoclinism	isoclinic class of D₂₁
automorphism	?
homology	Abelianization (H₁) = C₂×C₃² · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃²×D₂₁
unambiguous semidirect product	C₃⋊(C₃²×D₇)

	subgroup	G/H
center, hypercenter	C₃²	D₂₁
commutator, cosocle, hypocenter	C₃×C₇	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃³×C₇	C₂
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₃²

64 conjugacy classes of subgroups.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 126

A minimal faithful permutation representation — 2 generators on 16 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(378, 55);