order	204
isoclinism	isoclinic class of A₄
automorphism	Aut(G) = C₁₆×S₄ (order 384) · Inn(G) = A₄ · Out(G) = C₂×C₁₆
homology	Abelianization (H₁) = C₃×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

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

Splittings

Fitting, socle, Hall	C₂²×C₁₇ ⋊ C₃
derived, Sylow	C₂² ⋊ C₃×C₁₇

	subgroup	G/H
center, hypercenter	C₁₇	A₄
commutator, cosocle, hypocenter	C₂²	C₃×C₁₇
Frattini	C₁	G
Fitting, socle	C₂²×C₁₇	C₃
LCS	G ▷ C₂²
UCS	C₁ ◁ C₁₇

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(204, 8);