C₃×D₅₁ #64562

order	306
isoclinism	isoclinic class of D₅₁
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×D₅₁
unambiguous semidirect product	C₃⋊(C₃×D₁₇)
unambiguous semidirect product	C₁₇⋊(C₃×D₃)

	subgroup	G/H
center, hypercenter	C₃	D₅₁
commutator, cosocle, hypocenter	C₃×C₁₇	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃²×C₁₇	C₂
LCS	G ▷ C₃×C₁₇
UCS	C₁ ◁ C₃

18 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 102

A minimal faithful permutation representation — 2 generators on 23 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(306, 7);