Dic₃×D₁₇ #87970

order	408
isoclinism	isoclinic class of D₃×D₁₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

Dic₃×D₁₇

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃×D₁₇
commutator, hypocenter	C₃×C₁₇	C₂×C₄
Fitting, socle, cosocle	C₂×C₃×C₁₇	C₂²
prime radical	C₂×C₃×D₁₇	C₂
LCS	G ▷ C₃×C₁₇
UCS	C₁ ◁ C₂

32 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 204

A minimal faithful permutation representation — 2 generators on 24 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(408, 7);