C₃×#2449 #84313

order	384
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃ · Schur multiplier (H₂) = C₂⁵

Aliases

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃
prime radical	C₂²×C₃×D₄	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ G

648 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 16889);