C₂²×#803 #82043

order	384
isoclinism	isoclinic class of Dic₆
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁶

Aliases

680 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 384

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 14619);