C₃²×D₁₉ #66795

order	342
isoclinism	isoclinic class of D₁₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₃² · Schur multiplier (H₂) = C₃

Aliases

C₃²×D₁₉

Fitting, socle, Hall	C₃²×C₁₉ ⋊ C₂
derived, Sylow	C₁₉ ⋊ C₂×C₃²

	subgroup	G/H
center, hypercenter	C₃²	D₁₉
commutator, cosocle, hypocenter	C₁₉	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃²×C₁₉	C₂
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₃²

24 conjugacy classes of subgroups.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 171

A minimal faithful permutation representation — 2 generators on 25 points:

(4,5,6)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25);(1,2,3)(7,8,10,12,14,16,18,20,22,24,25,23,21,19,17,15,13,11,9)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(342, 13);