C₄×#887 #73615

order	384
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

C₃ ⋊ C₄²×Q₈

684 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 6191);