C₄×#877 #73433

order	384
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂³×C₄²

Aliases

752 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)(8,9,10,11)(14,18)(16,19);(12,14)(13,16)(15,18)(17,19);(2,3)(12,13,15,17)(14,16,18,19);(4,5,6,7)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 6009);