C₃×#2434 #84298

order	384
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃ · Schur multiplier (H₂) = C₂⁶

Aliases

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃
prime radical	C₂⁴×C₃	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ G

800 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 192

A minimal faithful permutation representation — 4 generators on 19 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 16874);