C₃³×D₇ #67400

order	378
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₃³ · Schur multiplier (H₂) = C₃³

Aliases

C₃³×D₇

Fitting, socle, Hall	C₃³×C₇ ⋊ C₂
derived, Sylow	C₇ ⋊ C₂×C₃³

	subgroup	G/H
center, hypercenter	C₃³	D₇
commutator, cosocle, hypocenter	C₇	C₂×C₃³
Frattini	C₁	G
Fitting, socle	C₃³×C₇	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₃³

112 conjugacy classes of subgroups.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 189

A minimal faithful permutation representation — 3 generators on 16 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(378, 53);