C₄×#815 #69748

order	384
isoclinism	isoclinic class of Dic₆
automorphism	?
homology	Abelianization (H₁) = C₄³ · Schur multiplier (H₂) = C₂×C₄²

Aliases

360 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 3 generators on 19 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 2324);