A₄×D₁₇ #88001

order	408
isoclinism	isoclinic class of A₄×D₁₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	A₄×D₁₇
unambiguous semidirect product	C₁₇⋊(C₂×A₄)
unambiguous semidirect product	(C₂²×D₁₇)⋊C₃

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₂²×C₁₇	C₂×C₃
LCS	G ▷ C₂²×C₁₇
UCS	C₁

24 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 68

A minimal faithful permutation representation — 2 generators on 21 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(408, 38);