C₂×C₃×D₁₆ #5379

order	192
nilpotency class	4
isoclinism	isoclinic class of D₁₆
automorphism	Aut(G) = C₂×#72213937 (order 2048) · Inn(G) = D₈ · Out(G) = C₂×#525
homology	Abelianization (H₁) = C₂³×C₃ · Schur multiplier (H₂) = C₂³

Aliases

C₂×C₃×D₁₆

	subgroup	G/H
center, socle	C₂²×C₃	D₈
commutator, Frattini, cosocle	C₈	C₂³×C₃
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₈ ◁ G

98 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 96

A minimal faithful permutation representation — 3 generators on 21 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 938);